We provide algebraic expressions and identities practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on algebraic expressions and identities skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.
List of algebraic expressions and identities Questions
| Question No | Questions | Class |
|---|---|---|
| 1 | Simplify: ( (boldsymbol{x}+mathbf{5})(boldsymbol{x}+mathbf{4}) ) A ( cdot x^{2}+27 x+20 ) B . ( x^{2}+9 x+20 ) c. ( x^{2}+18 x+20 ) D. ( x^{2}+x+20 ) | 8 |
| 2 | Subtract the second expression from the first: ( 5 x^{2}+4 y^{2}-6 y+8 ) and ( x^{2}-5 y^{2}+ ) ( 2 x y+3 y-10 ) A ( cdot 4 x y^{2}+9 x y^{2}+9 y-2 y+12 ) В. ( 4 x^{y}+9 y^{3}+9 y+2 x y+18 ) c. ( 4 x^{2}+9 y^{2}-9 y-2 x y+18 ) D. ( x^{2}+9 y^{2}-9 y-2 x y+12 ) | 8 |
| 3 | Simplify ( 2(3 b-5 a)-7[9- ) ( 62-5(a-6)] ) | 8 |
| 4 | What should be added to ( 6 x^{2}-3 x y+ ) ( 4 y^{2} ) to get ( 2 y^{2}+x y-4 x^{2} ? ) A. ( -x^{2}-y^{2}+4 y ) B . ( -10 x^{2}-y^{2}+4 x y ) c. ( x^{2}-2 y^{2}+4 x ) D. ( -10 x^{2}-2 y^{2}+4 x y ) | 8 |
| 5 | Add the following algebraic expressions: (i) ( 2 x^{2}+3 x+5,3 x^{2}-4 x-7 ) (ii) ( x^{2}-2 x-3, x^{2}+3 x+1 ) (iii) ( 2 t^{2}+t-4,1-3 t-5 t^{2} ) (iv) ( boldsymbol{x y}-boldsymbol{y} boldsymbol{z}, boldsymbol{y} boldsymbol{z}-boldsymbol{x} boldsymbol{z}, boldsymbol{z} boldsymbol{x}-boldsymbol{x} boldsymbol{y} ) ( (v) a^{2}+b^{2}, b^{2}+c^{2}, c^{2}+a^{2}, 2 a b+ ) ( 2 b c+2 c a ) | 8 |
| 6 | Expand the polynomial: ( left(3 x^{2}-1right)left(x^{2}+right. ) ( boldsymbol{x}+mathbf{1}) ) A ( cdot 3 x^{4}+3 x^{3}+3 x^{2}+x^{2}-x-1 ) B. ( 3 x^{4}+3 x^{3}+x^{2}-x^{2}-x-1 ) c. ( 3 x^{4}+3 x^{3}+2 x^{2}-x-1 ) D. ( 3 x^{4}-3 x^{3}+3 x^{2}-x^{2}-x-1 ) | 8 |
| 7 | ( sqrt{2 x-3}+sqrt{7-3 x} ) | 8 |
| 8 | Simplify: ( sqrt{boldsymbol{x}^{2}}+sqrt{boldsymbol{y}^{2}}-boldsymbol{x}-boldsymbol{y}+ ) ( sqrt{(boldsymbol{a}+boldsymbol{b})^{2}} ) | 8 |
| 9 | How much is ( x+3 y-4 z ) greater than ( 3 x-2 y+z ? ) | 8 |
| 10 | Subtract : ( -x^{2}+y^{2}-x^{2} y+5 x y^{2} ) from ( x^{2}+ ) ( x^{2} y-5 x y^{2}-y^{2} ) | 8 |
| 11 | Simplify: ( boldsymbol{x}^{2}left(boldsymbol{3}-boldsymbol{5} boldsymbol{y}^{2}right)+ ) ( boldsymbol{x}left(boldsymbol{x} boldsymbol{y}^{2}-boldsymbol{3} boldsymbol{x}right)-boldsymbol{2} boldsymbol{y}left(boldsymbol{y}-boldsymbol{2} boldsymbol{x}^{2} boldsymbol{y}right) ) A ( cdot 6 x^{2}-2 y^{2}-3 x^{2} y ) В. ( 6 x^{2} ) ( mathrm{c} cdot 3 x^{2} y ) D. ( -2 y^{2} ) | 8 |
| 12 | Addition of ( left(x^{2}+y^{2}right) ) and ( left(x^{2}-y^{2}right) ) is | 8 |
| 13 | 69. If a + b2 + c = ab + bc + ca, a + c is then the value of h (1) 3 (2) 2 (3) o (4) 1 | 8 |
| 14 | Add: ( 6 a x-2 b y+3 c z, 6 b y-11 a x-c z ) and ( 10 c z-2 a x-3 b y ) | 8 |
| 15 | Solve : ( left(x^{2}+4 x yright)+left(4 y^{2}-9 z^{2}right) ) | 8 |
| 16 | If ( 2 x^{2}+x y-3 y^{2}+x+a y-10= ) ( (2 x+3 y+b)(x-y-2), ) the value of a and b are A. 11 and 5 B. 1 and -5 c. -1 and -5 D. -11 and 5 | 8 |
| 17 | State whether the statement is True or False. ( (x+8)(x+3) ) is equal to ( x^{2}+11 x+ ) ( mathbf{2 4} ) A. True B. False | 8 |
| 18 | Simplify ( left(a^{3}-2 a^{2}+4 a-5right)- ) ( left(-a^{3}-8 a+2 a^{2}+5right) ) A ( cdot 2 a^{3}+7 a^{2}+6 a-10 ) В. ( 2 a^{3}+7 a^{2}+12 a-10 ) c. ( 2 a^{3}-4 a^{2}+12 a-10 ) D . ( 2 a^{3}+4 a^{2}+6 a-10 ) | 8 |
| 19 | Simplify the polynomial and write it in standard form: ( (-2 x-5)(2 x-8)-(2 x-5)(3 x+7) ) | 8 |
| 20 | 65. For real a, b, c if a + b + c = ab a + c + bc + ca, then value of *° is (1) 1 (2) 2 (3) 3 (4) O | 8 |
| 21 | Factorise : ( z^{2}-left(x^{2}-2 x y+y^{2}right) ) | 8 |
| 22 | What should be added to ( x^{2}+x y+y^{2} ) to obtain ( 2 x^{2}+3 x y ? ) | 8 |
| 23 | If ( 3 x+5 y=4, ) which of the following is equivalent to the expression ( (6 x+ ) ( (10 y)(100 x+100 y) ? ) A. ( 100 x+100 y ) в. ( 200 x+200 y ) c. ( 400 x+400 y ) D. ( 800 x+800 y ) E . ( 1,600 x+1,600 y ) | 8 |
| 24 | Solve ( left(boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1}right)left(boldsymbol{x}^{4}+boldsymbol{x}^{3}+boldsymbol{x}+mathbf{1}right) ) | 8 |
| 25 | Solve ( left(3 x^{2}+4 yright) times(2 x+3 y) ) | 8 |
| 26 | State True or False: Addition of ( 5 a+3 b, a-2 b, 3 a+5 b ) is ( 9 a+6 b ) A. True B. False | 8 |
| 27 | Subtract ( 5 x y ) from ( 8 x y ) | 8 |
| 28 | Find the constant after subtracting from ( x^{4}+4 x^{2}-3 x+7 ) to get ( 3 x^{3}- ) ( x^{2}+2 x+1 ? ) | 8 |
| 29 | Subtract ( 4 p^{2} q-3 p q+5 p q^{2}-8 p+ ) ( 7 q-10 ) from ( 18-3 p-11 q+5 p q ) ( 2 q^{2}+5 p^{2} q ) A ( cdot 28+5 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} ) B . ( 8+11 p-18 q+8 p q-2 q^{2}+p^{2} q-5 p q^{2} ) C. ( 28-5 p+18 q-8 p q+2 q^{2}-p^{2} q+5 p q^{2} ) D. none | 8 |
| 30 | If ( boldsymbol{P}=mathbf{3} boldsymbol{x}-mathbf{4} boldsymbol{y}-mathbf{8} boldsymbol{z}, boldsymbol{Q}=-mathbf{1 0} boldsymbol{y}+ ) ( 7 x+11 z ) and ( R=19 z-6 y+4 x, ) then ( boldsymbol{P}-boldsymbol{Q}+boldsymbol{R} ) is equal to A ( .13 x-20 y+16 z ) B. 0 c. ( x+y+z ) D. ( 2 x-b y+3 z ) | 8 |
| 31 | ( left(6 x^{2}-5 yright)^{2} ) Find square by identity | 8 |
| 32 | Find the product of ( x^{2} y z times x y^{2} z^{3} ) A ( cdot x^{3} y^{3} z^{4} ) В. ( x^{3} y^{3} z^{3} ) c. ( x^{3} y^{4} z^{3} ) D. ( x^{3} y^{3} z ) | 8 |
| 33 | Add all of them ( x-8 y, 3 x y-y ) and ( boldsymbol{y}+mathbf{1} ) | 8 |
| 34 | Show that – (i) ( (2 a+3 b)^{2}-(2 a-3 b)^{2}=24 a b ) (ii) ( (4 x+5)^{2}-80 x=(4 x-5)^{2} ) | 8 |
| 35 | If ( boldsymbol{A}=mathbf{5} boldsymbol{p}^{2}-boldsymbol{3} boldsymbol{q}^{2}+boldsymbol{r}^{2}, boldsymbol{B}=-boldsymbol{2} boldsymbol{q}^{2}+ ) ( boldsymbol{3} boldsymbol{p}^{2}-boldsymbol{4} boldsymbol{r}^{2} ) and ( boldsymbol{C}=-boldsymbol{7} boldsymbol{r}^{2}+boldsymbol{3} boldsymbol{p}^{2}+boldsymbol{2} boldsymbol{q}^{2} ) Find ( boldsymbol{A}+boldsymbol{B}-boldsymbol{C} ) | 8 |
| 36 | Subtract ( 24 a b-10 b-18 a ) from ( 30 a b+12 b+14 a ) | 8 |
| 37 | Which rational expression should be added to ( frac{x-x^{2}+2}{xleft(x^{2}-1right)} ) to get ( frac{x+1}{x^{2}-1} ? ) A ( cdot frac{x}{2} ) B. ( frac{2}{x} ) c. ( 2 x ) D. ( x^{2} ) | 8 |
| 38 | ( frac{a}{a-c}+frac{b}{b-c} ) | 8 |
| 39 | 51. The sum of two numbers is 37 and the difference of their squares is 185. then the differ- ence between the two numbers is : (1) 10 (2) 4 (3) 5 (4) 3 | 8 |
| 40 | Simplify combining like terms. ( 21 b-32+7 b-20 b ) | 8 |
| 41 | Add the given expression: ( 5 sqrt{x}- ) ( 4 sqrt{y}+2 ; 2 sqrt{x}+7 sqrt{y}-5 ) A. ( 7 sqrt{x}+3 sqrt{y}-3 ) В. ( 7 sqrt{x}+3 sqrt{y}-5 ) c. ( 7 sqrt{x}+3 sqrt{y}-8 ) D. ( 7 sqrt{x}+2 sqrt{y}-3 ) | 8 |
| 42 | From the sum of ( 3 x-y+11 ) and ( -y- ) 11 subtract ( 3 x-y-11 ) | 8 |
| 43 | What should be added to ( frac{1}{x}, ) to make it equal to ( x ? ) A. ( frac{x^{2}-x}{x^{2}} ) в. ( frac{x}{x^{2}-1} ) c. ( frac{x^{2}+1}{x} ) D. ( frac{x^{2}-1}{x} ) | 8 |
| 44 | What should be added to ( 5 x^{2}+2 x y+ ) ( y^{2} ) to get ( 3 x^{2}+4 x y ? ) A. ( -2 x^{2}+2 x y-y^{2} ) B . ( x^{2}+2 y-y^{2} ) C ( .-2 x^{2}+2 y-x y^{2} ) D. ( x^{2}+2 x y-y^{2} ) | 8 |
| 45 | State True or False: On subtracting ( a-b-2 c ) from ( 4 a+ ) ( 6 b-2 c, ) the answer is ( 3 a+7 b ) A. True B. False | 8 |
| 46 | Simplify: ( (3.5 e-4.5 f)(1.5 e+4 f+ ) ( e f)-4.5 e+10 f ) | 8 |
| 47 | Find the expression equivalent to ( frac{1}{2} y^{2}(6 x+2 y+12 x-2 y) ) A ( cdot 9 x y^{2} ) ( begin{array}{ll}2 & 2 \ 2 & 2end{array} ) в. ( 18 x y ) c. ( 3 x y^{2}+12 x ) D. ( 9 x y^{2}-2 y^{3} ) E ( .3 x y^{2}+12 x-y^{3}-2 y ) | 8 |
| 48 | Give expressions in the following cases. ( boldsymbol{y} ) is multiplied by 5 and results is subtracted from 16. | 8 |
| 49 | Multiply: ( left(m^{2}-5right) timesleft(m^{3}+2 m-2right) ) | 8 |
| 50 | select a suitable identity and find the following products ( left(a x^{2}+b y^{2}right)left(a x^{2}+b y^{2}right) ) | 8 |
| 51 | Find the product of ( 3 x^{3} y^{2} ) and ( (2 x-3 y) ) Also, verify the result for ( boldsymbol{x}=-mathbf{1}, boldsymbol{y}=mathbf{2} ) | 8 |
| 52 | Substract ( x^{2} ) from ( x^{2}+y^{2}-3 y ) | 8 |
| 53 | How much more than ( 2 x^{2}+4 x y+2 y^{2} ) is ( 5 x^{2}+10 x y-y^{2} ? ) State True or False: The answer is ( 3 x^{2}+ ) ( 6 x y-3 y^{2} ) A . True B. False | 8 |
| 54 | Evaluate: ( left(4 x^{2}-frac{1}{5} x+7right)- ) ( left(-2 x^{2}-frac{1}{2} x+frac{1}{3}right) ) | 8 |
| 55 | Subtract. ( 5 a^{2}-7 a b+5 b^{2} ) from ( 3 a b-2 a^{2}-2 b^{2} ) | 8 |
| 56 | ( (n-10)^{2}+(10-n) ) | 8 |
| 57 | By how much does ( x^{2}-2 a x+5 ) exceed ( 3 x^{2}-5 x+6 ? ) | 8 |
| 58 | Simplify combining like terms: ( 5 x^{2}-5 x^{2}+3 y x^{2}-3 y^{2}+x^{2}-y^{2}+ ) ( 8 x y^{2}-3 y^{2} ) | 8 |
| 59 | Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively ( (p, q) ;(10 m, 5 n) ;left(20 x^{2}, 5 y^{2}right) ;left(4 x, 3 x^{2}right) ) A ( cdot 100 x^{2} y^{2} ; 12 x^{3} ; 12 m n^{2} p ) B . ( 100 x^{2} y^{2} ; 12 x^{2} ; 12 m n^{2} p ) C ( cdot 100 x^{2} y ; 12 x^{3} ; 12 m n^{2} p ) D. ( 100 x^{2} y^{2} ; 12 x^{3} ; 12 m n p ) | 8 |
| 60 | Simplify: ( left(boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1}right)left(mathbf{2} boldsymbol{x}^{2}+mathbf{2}right) ) A ( cdot 2 x^{4}-2 x^{3}+4 x^{2}-2 x+2 ) B . ( 2 x^{4}-2 x^{3}+4 x^{5}-2 x+2 ) c. ( 2 x^{4}+2 x^{3}+4 x^{2}-2 x+2 ) D. ( 2 x^{4}-2 x^{3}-2 x+2 ) | 8 |
| 61 | Simplify: ( 25 a b c^{2}-15 a^{2} b^{2} c ) | 8 |
| 62 | Evaluate: ( (l+m)-4 m ) | 8 |
| 63 | Add the following algebraic expression using both horizontal and vertical methods. Did you get the same answer with both methods ( x^{2}-2 x y+3 y^{2} ; 5 y^{2}+3 x y-6 x^{2} ) | 8 |
| 64 | The length and breadth and height of a cuboid are ( (x+3),(x-2) ) and ( (x-1) ) respectively. Find its volume. | 8 |
| 65 | Which polynomial should be added to ( 2 x^{4}-3 x^{2}+5 x+8 ) to get ( 2 x^{2}-5 x+4 ) ( ? ) A ( cdot x^{3}+5 x^{2}-x ) B . ( 2 x^{5}+x^{2}-10 x-9 ) c. ( -2 x^{4}+5 x^{2}-1 ) D. ( -2 x^{4}+5 x^{2}-10 x-4 ) | 8 |
| 66 | Add ( 8 x y+4 y z-7 z x, 6 y z+11 z x- ) ( 6 y ) and ( -5 x z+6 x-2 y x ) | 8 |
| 67 | Add ( a+b-3, b-a+3, a-b+3 ) | 8 |
| 68 | Simplify : ( x y+left(x y+4 x^{3}+3 x-5right)-left(-3 x^{2}-right. ) 4) ( -left(x y+x^{3}-4right) ) | 8 |
| 69 | State True or False: Addition of ( a^{6}-4 a^{4}+6 a, 5 a^{6}+ ) ( mathbf{5} a^{4}+mathbf{6 a}, mathbf{1 2 a}^{mathbf{6}}-mathbf{1 0 a} ) is ( mathbf{1 8 a}^{mathbf{6}}+boldsymbol{a}^{mathbf{4}}+ ) ( mathbf{2} boldsymbol{a} ) A. True B. False | 8 |
| 70 | ( 9 x^{2}-y^{2}+4 y-4 ) | 8 |
| 71 | If ( 49 x^{2}-b=left(7 x+frac{1}{2}right)left(7 x-frac{1}{2}right), ) then the value of ( b ) is ( mathbf{A} cdot mathbf{0} ) в. ( frac{1}{sqrt{2}} ) ( c cdot frac{1}{4} ) D. | 8 |
| 72 | State True or False ( 13 m^{2}-2 m^{2}=11 m^{2} ) A. True B. False | 8 |
| 73 | Subtract the second expression from the first expression ( boldsymbol{x}+mathbf{2} boldsymbol{y}+boldsymbol{z},-boldsymbol{x}-boldsymbol{y}-mathbf{3} boldsymbol{z} ) | 8 |
| 74 | Add the followign: ( 13 x^{2},-31 x^{2}, 25 x^{2} ) | 8 |
| 75 | Add the following expressions: ( boldsymbol{a}+boldsymbol{b}-mathbf{3}, boldsymbol{b}-boldsymbol{a}+mathbf{3}, boldsymbol{a}-boldsymbol{b}+mathbf{3} ) | 8 |
| 76 | Simplify: ( left(-10 a^{3} b+12 a^{2} b^{2}-6 a b^{3}right)- ) ( left(8 a^{3} b+6 a^{2} b^{2}-9 a b^{3}right) ) | 8 |
| 77 | Simplify: ( (2 p+3 q+4 r)(9 p-r)+(p+q+r) ) | 8 |
| 78 | Add ( left(6 a b^{3}-5 a bright)left(2 a^{2}+b-right. ) 5) ( , a bleft(a^{2}+1right) ) and ( a b^{3}left(3 a^{3}+2 b+1right) ) | 8 |
| 79 | Simplify ( (a+b)(c-d)+(a-b)(c+d) ) | 8 |
| 80 | Form an equation ( a x^{2}+b x y+c y^{2} ) by subtracting the sum of ( x^{2}-5 x y+2 y^{2} ) and ( y^{2}-2 x y-3 x^{2} ) from the sum of ( 6 x^{2}-8 x y-y^{2} ) and ( 2 x y-2 y^{2}-x^{2} ) Find ( boldsymbol{a}+boldsymbol{b}+boldsymbol{c} ) | 8 |
| 81 | Add: ( a+b+a b ; b-c+b c ) and ( c+ ) ( a+a c ) | 8 |
| 82 | Find the following product: ( left(x^{3}-5 x^{2}+right. ) ( 3 x+1) timesleft(x^{2}-3right) ) A ( cdot x^{5}-5 x^{4}+16 x^{2}-9 x+3 ) B. ( x^{5}-5 x^{4}+16 x^{2}+9 x-3 ) c. ( x^{5}+5 x^{4}+16 x^{2}-9 x-3 ) D. ( x^{5}-5 x^{4}+16 x^{2}-9 x-3 ) | 8 |
| 83 | Simplify the algebraic expression: ( 2 x- ) ( [3 y+{5 x-(3 y-2 x)}-2] ) | 8 |
| 84 | ( f(a+b+c=27, ) then what is the value of ( (a-7)^{3}+(b-9)^{3}+(c-11)^{3}- ) ( mathbf{3}(boldsymbol{a}-mathbf{7})(boldsymbol{b}-mathbf{9})(boldsymbol{c}-mathbf{1 1}) ? ) A . 0 B. 9 c. 27 D. 81 | 8 |
| 85 | Multiply: ( left(4 x^{4}-3 x^{2}-7 x+8right) ) by ( left(5 x^{2}-2 x-3right) ) Answer: ( 20 x^{6}-8 x^{5}-27 x^{4}-29 x^{3}+ ) ( 63 x^{2}+5 x-24 ) A. True B. False | 8 |
| 86 | Prove that: ( frac{1}{1+x^{a-b}}+frac{1}{1+x^{b-a}}=1 ) | 8 |
| 87 | Find the value of the addition of ( (x- ) ( 3 y+4 z),(y-2 x-8 z),(5 x-2 y- ) ( 3 z) ) | 8 |
| 88 | 62. If x + y + z =9 and x2 + y2 +22= 35, then the value of xº + y2 + 2 – 3xyz is : (1) 105 (2) 108 (3) 109 (4) 125 | 8 |
| 89 | ( (x-6)+(3 x-4)+(x-1) ) | 8 |
| 90 | Find the expansion of ( (3 x+1)(3 x+2)(3 x+5) ) A ( cdot 27 x^{3}+72 x^{2}+51 x+10 ) B. ( 27 x^{3}-72 x^{2}+51 x+10 ) c. ( 27 x^{3}+72 x^{2}-51 x+10 ) D. None of these | 8 |
| 91 | ( boldsymbol{x}+boldsymbol{y}- ) ( (z-x-[y+z-(x+y-{z+x-(y ) is equal to A . ( x ) B. ( 2 y ) c. D. | 8 |
| 92 | State True or False: Addition of ( a-3 b+3,2 a+5 ) ( mathbf{3 c}, mathbf{6 c}-mathbf{1 5}+mathbf{6 b} ) is ( mathbf{3 a}+mathbf{3 b}+mathbf{3 c – 7} ) A. True B. False | 8 |
| 93 | Multiply: ( (x-2)left(x^{2}+3 x+7right) ) A ( cdot x^{3}+2 x^{2}+6 x-14 ) B. ( x^{3}+x^{2}+6 x-14 ) c. ( x^{3}+x^{2}+x-14 ) D. ( x^{3}+2 x^{2}+3 x-14 ) | 8 |
| 94 | Evaluate ( a^{2}-b^{2}-(a+b)^{2} ) | 8 |
| 95 | Find the expansion of ( (p+2)(p-4)(p+6) ) A ( cdot p^{3}+4 p^{2}-20 p-48 ) в. ( p^{3}-4 p^{2}-20 p-48 ) c. ( p^{3}+4 p^{2}+20 p-48 ) D. None of these | 8 |
| 96 | In a school, ( 8 a^{2}+4 a+9 ) students were enrolled. ( 2 a^{2}-9 a+2 ) students were boys. How many girls were enrolled? A ( cdot 6 a^{2}-13 a+7 ) 7 B . ( 4 a^{2}+13 a+7 ) ( mathbf{c} cdot 6 a^{2}+13 a+7 ) D. ( 4 a^{2}-13 a+7 ) | 8 |
| 97 | What must be added to ( 7 z^{3}-11 z^{2}- ) 129 to ( operatorname{get} 5 z^{2}+7 z-92 ? ) A ( cdot 7 z^{3}+16 z^{2}+7 z+37 ) B . ( -7 z^{3}+16 z^{2}+7 z+37 ) D. ( -7 z^{3}-7 z^{2}+7 z-37 ) | 8 |
| 98 | Find each of the following products. ( 6 a times 4 b^{2} ) | 8 |
| 99 | Simplify: ( 4(x-5) ) A ( .4 x-5 ) B. ( 4 x-20 ) c. ( 4 x+5 ) D. ( 4 x+20 ) | 8 |
| 100 | If ( frac{a^{3}+3 a b^{2}}{3 a^{2} b+b^{3}}=frac{x^{3}+3 x y^{2}}{3 x^{2} y+y^{3}}, ) then A ( cdot b x=a y ) в. ( b y=a x ) ( mathbf{c} cdot b^{2} y=a^{2} x ) D. ( b^{2} x=a^{2} y ) | 8 |
| 101 | From the sum of ( 3 x-y+11 ) and ( -y- ) 11, subtract the sum of ( 3 x^{2}-5 x ) and ( -x^{2}+2 x+5 ) | 8 |
| 102 | Subtract ( 3 x y+2 z^{2} ) from ( 5 x y+3 z^{2}- ) ( x z ) | 8 |
| 103 | Simplify ( (boldsymbol{x}+boldsymbol{y})(boldsymbol{x}-boldsymbol{y})+(boldsymbol{2} boldsymbol{x}- ) ( boldsymbol{y})(boldsymbol{3} boldsymbol{x}+boldsymbol{y}) ) A ( cdot 7 x^{2}-2 y^{2}-x y ) В. ( x^{2}-y^{2}+x y ) c. ( 7 x^{2}-2 y^{2}+x y ) D. ( x^{2}-2 y^{2}+x y ) | 8 |
| 104 | Evaluate: ( 8left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}+x^{2} y^{2} z^{2}right) ) ( 4 x^{2} y^{2} z^{2} ) | 8 |
| 105 | The sum of three expressions is ( x^{2}+ ) ( y^{2}+z^{2} . ) If two of them are ( 4 x^{2}-5 y^{2}+ ) ( 3 z^{2} ) and ( -3 x^{2}+4 y^{2}+2 z^{2}, ) the third expression is A ( cdot 2 x^{2}+2 z^{2} ) в. ( 2 y^{2} ) c. ( 2 x^{2}+2 y^{2}-z^{2} ) D. ( 2 y^{2}-4 z^{2} ) | 8 |
| 106 | The perimeter of a triangle is ( 8+ ) ( 13 a+7 a^{2} ) and two of its sides are ( 2 a^{2}+3 a+2 ) and ( 3 a^{2}-4 a-1 . ) Find the third side of the triangle. | 8 |
| 107 | ( boldsymbol{x}+boldsymbol{y}- ) ( (z-x-[y+z-(x+y-{z+x-(y ) is equal to A . ( 3 x ) B. ( 2 y ) c. ( x ) D. | 8 |
| 108 | ( -8 y z times-2 x y= ) A . ( 16 x y z ) B . ( -16 x y^{2} z ) c. ( 16 x y^{2} z ) D. ( -16 x^{2} y^{2} z^{2} ) | 8 |
| 109 | Give expressions in the following cases. 11 added to ( 2 m ) | 8 |
| 110 | Subtract: ( a(b-5) ) from ( b(5-a) ) | 8 |
| 111 | Simplify: ( y(x-2 y)^{2}-13+4(x-1) ) | 8 |
| 112 | What should be subtracted from ( x^{3}- ) ( 7 x^{2}+17 x+17 ) so that the difference is a multiple of ( x-3 ? ) A . 5 B. 32 ( c cdot 7 ) D. 43 | 8 |
| 113 | Simplify the expression: ( t^{2}-59 t+ ) ( 54-82 t^{2}+60 t ) ( mathbf{A} cdot-26 t^{2} ) B . ( -26 t^{6} ) c. ( -81 t^{4}+t^{2}+54 ) D. ( -81 t^{2}+t+54 ) | 8 |
| 114 | By how much does ( 3 x-4 x y+2 z ) exceed ( 8 x+5 z-7 x y ? ) | 8 |
| 115 | Solve: Add ( 3 a(a-b+c), 2 b(a-b+c) ) | 8 |
| 116 | What should be taken away from ( 3 x^{2}- ) ( 4 y^{2}+5 x y+20 ) to ( operatorname{get}-x^{2}-y^{2}+ ) ( 6 x y+20 ) A ( cdot x^{2}-y^{2}-x y ) в. ( x^{3}-3 y^{2}-x y ) c. ( x^{2}-y^{3}-x y ) D. ( 4 x^{2}-3 y^{2}-x y ) | 8 |
| 117 | Simplify : ( 3 a-2 b-a b-(a-b+a b)+3 a b+ ) ( boldsymbol{b}-boldsymbol{a} ) | 8 |
| 118 | Simplify: ( (2 x+1)(1-x)left(x^{2}+xright) ) A ( cdot 2 x^{4}-x^{3}+2 x^{2}+x ) В. ( -2 x^{4}-x^{3}+2 x^{2}+x ) c. ( -2 x^{4}+x^{3}+2 x^{2}+x ) D. ( -2 x^{4}-x^{3}+2 x^{2}-x ) | 8 |
| 119 | Subtract the following: ( boldsymbol{p}(boldsymbol{y})=boldsymbol{3} boldsymbol{y}^{7}-boldsymbol{2} boldsymbol{y}^{2}+boldsymbol{3} ) and ( boldsymbol{q}(boldsymbol{y})=boldsymbol{y}^{7}+ ) ( boldsymbol{y}^{2}+boldsymbol{y} ) | 8 |
| 120 | solve ( boldsymbol{a}^{boldsymbol{7}}+frac{mathbf{1}}{boldsymbol{a}^{boldsymbol{9}}}=? ) | 8 |
| 121 | Solve: ( frac{boldsymbol{x}+mathbf{2 0}}{mathbf{9}}+frac{mathbf{3} boldsymbol{x}}{mathbf{7}}=mathbf{6} ) | 8 |
| 122 | Add the expressions in each of the following. i) ( 2 l+3 m-6 n+4 p, 3 l-5 m+ ) ( 16 n-4 p, 12 l-6 m-4 n-2 p a n d l- ) ( 2 m+3 n-4 p ) ii) ( 7 x^{3}+3 x+9,-2 x^{3}-3 x^{2}- ) ( 15,3 x^{3}-6 x^{2}+4 x-6 a n d 12 x^{2}-6 ) iii) ( 5 a^{2}-7 a b+9 b^{2}, 4 a^{2}-2 b^{2}- ) ( 9 a b-6,4-3 b^{2}+2 a b+ ) ( 6 a^{2} ) and ( 12 a b-3 a^{2}-9 b^{2} ) | 8 |
| 123 | ( left(frac{2}{5} a b+cright)left(frac{2}{5} a b-cright) ) is equal to A ( cdot frac{4}{25} a^{2} b^{2}-frac{4}{5} a b c+c^{2} ) B ( cdot frac{4}{25} a^{2} b^{2}+frac{4}{5} a b c+c^{2} ) C ( frac{4}{25} a^{2} b^{2}-c^{2} ) D ( cdot frac{4}{25} a^{2} b^{2}+c^{2} ) | 8 |
| 124 | ( x^{2}-2 x+1 ; 2 x ) multiply this polynomial | 8 |
| 125 | How much does ( -5 a^{2}+3 a-5 b^{2} ) ( operatorname{exceed} 7 a^{2}+4 a-9 b^{2} ? ) | 8 |
| 126 | Which of the following relation is correct. A ( .3(x-9)=3 x-27 ) B. ( 3(x-9)=3 x-24 ) c. ( 3(x-8)=3 x-27 ) D. None | 8 |
| 127 | Find the joint equation of the following pair of lines. ( x+2 y-1=0 ) and ( 2 x-3 y+2=0 ) | 8 |
| 128 | Simplify ( left(5 p^{2}-3right)+left(2 p^{2}-3 p^{3}right) ) | 8 |
| 129 | Factorize ( left(1+frac{1}{x}+frac{1}{x^{2}}+frac{1}{x^{3}}right) ) | 8 |
| 130 | Add the following (i) ( x-3 y-2 z ) ( 5 x+7 y-8 z ) ( 3 x-2 y+5 z ) | 8 |
| 131 | Subtract: ( a+2 b-c ) from ( 3 a-b+2 c ) | 8 |
| 132 | Factorize: ( 16 a^{4}-9 b^{4} ) | 8 |
| 133 | Simplify ( 12-left(x+x^{2}right)left(8-x-x^{2}right) ) | 8 |
| 134 | What should be added in ( frac{1}{x} ) so that the result ( x: ) A ( cdot frac{1-x^{2}}{x} ) в. ( frac{1-x}{x} ) c. ( frac{x^{2}-1}{x} ) D. | 8 |
| 135 | Subtract ( 4 a b c ) from ( -6 a b c ) | 8 |
| 136 | Find the continued products: ( (mathbf{i})(boldsymbol{x}+mathbf{2})(boldsymbol{x}-mathbf{2})left(boldsymbol{x}^{mathbf{2}}-mathbf{4}right) ) (ii) ( (a x+b)(a x-b)left(a^{2} x^{2}+b^{2}right) ) | 8 |
| 137 | Simplify 🙁 x^{2}+z^{2}-2 x z ) | 8 |
| 138 | Subtract the sum of ( left(5 x^{2}-7 x+4right) ) and ( left(2 x-5 x^{3}+1right) ) from ( left(3 x^{2}-1+5 xright) ) B. ( 5 x^{3}-2 x^{2}+10 x-6 ) ( c cdot 3 x^{3}+11 x^{2}+3 x+5 ) 5 D. ( 11 x^{3}+3 x^{2}+5 x-3 ) | 8 |
| 139 | Find the ( left[frac{7}{9} p^{2} q rright] timesleft(18 p q^{2}right)left(-frac{3}{14} r^{2}right) ) | 8 |
| 140 | Let for ( boldsymbol{a} neq boldsymbol{a}_{1} neq mathbf{0}, boldsymbol{f}(boldsymbol{x})=boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+ ) ( boldsymbol{c}, boldsymbol{g}(boldsymbol{x})=boldsymbol{a}_{1} boldsymbol{x}^{2}+boldsymbol{b}_{1} boldsymbol{x}+boldsymbol{c}_{1} ) and ( boldsymbol{p}(boldsymbol{x})= ) ( boldsymbol{f}(boldsymbol{x})-boldsymbol{g}(boldsymbol{x}), ) If ( boldsymbol{p}(boldsymbol{x})=mathbf{0} ) only for ( boldsymbol{x}= ) -1 and ( p(-2)=2, ) then the value of ( p(2) ) is : A . 3 B. 9 ( c cdot 6 ) D. 18 | 8 |
| 141 | State True or False: On subtracting ( -2 x^{2} y+3 x y^{2} ) from ( 8 x^{2} y, ) the answer is ( 10 x^{2} y-3 x y^{2} ) A. True B. False | 8 |
| 142 | Multiply: ( -5 c d^{2} ) by ( -5 c d^{2} ) ( mathbf{A} cdot 25 c^{2} d^{5} ) ( mathbf{B} cdot 25 c^{3} d^{4} ) ( mathbf{C} cdot 25 c^{2} d^{3} ) D. ( 25 c^{2} d^{4} ) | 8 |
| 143 | Subtract the sum of ( 36-4 m-7 x^{2} ) and ( 2 t-3 m-4 x^{2} ) from the sum of ( 96+2 m-3 x^{2} ) and ( -36+m+4 x^{2} ) | 8 |
| 144 | If ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{2}, ) then what is the value of ( boldsymbol{x}^{64}+boldsymbol{x}^{121} ? ) ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) D. – – | 8 |
| 145 | What should be added to ( x^{2}+x y+y^{2} ) to obtain ( 2 x^{2}+3 x y ) | 8 |
| 146 | Given that ( 13 x+7 ) is equal to ( -9-3 x ) the value of ( x ) is ( A cdot 8 ) в. ( frac{1}{5} ) ( c cdot frac{1}{8} ) D. – | 8 |
| 147 | Simpllify ( : 2 x^{2}+5 x-1+8 x+x^{2}+ ) ( 7-6 x+3-3 x^{2} ) | 8 |
| 148 | Simplify combining like terms: ( left(3 y^{2}+5 y-4right)-left(8 y-y^{2}-4right) ) | 8 |
| 149 | The product of ( frac{x^{2}-4}{x+1} ) and ( frac{2 x+2}{x-2} ) is A ( .2 x-4 ) B. 0 c. ( 2 x+4 ) D. | 8 |
| 150 | Evaluate: ( left(3 n^{2}-2 n+5 n^{4}+3right)(-6) ) A. ( -30 n^{4}+18 n^{2}-12 n-18 ) B. ( -30 n^{4}-18 n^{2}-12 n-18 ) c. ( 30 n^{4}-18 n^{2}-12 n-18 ) D. ( 30 n^{4}+18 n^{2}-12 n-18 ) | 8 |
| 151 | Find the difference between ( boldsymbol{P}(boldsymbol{x})= ) ( boldsymbol{x}^{4}-boldsymbol{3} boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+mathbf{5}, boldsymbol{g}(boldsymbol{x})=boldsymbol{x}^{2}+mathbf{1}-boldsymbol{x} ) | 8 |
| 152 | Simplify: ( boldsymbol{x}+mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{x} ) ( mathbf{A} cdot mathbf{5} ) B. ( 5 x ) ( c .6 ) D. ( 6 x ) | 8 |
| 153 | Evaluate ( 12(2 x-3 y)^{2}-16(3 y-2 x) ) | 8 |
| 154 | ( mathbf{5} boldsymbol{x}^{mathbf{3}}+mathbf{5} boldsymbol{x}^{mathbf{2}}+mathbf{4} boldsymbol{x}+mathbf{3}+mathbf{4} boldsymbol{x}^{mathbf{2}}+mathbf{5} boldsymbol{x}= ) A ( cdot 9 x^{3}+4 x^{2}+4 x+5 ) B . ( 5 x^{3}+5 x^{2}+9 x+4 ) ( mathbf{c} cdot 5 x^{3}+9 x^{2}+9 x+3 ) D. None of the above | 8 |
| 155 | What should be subtracted from ( 2 a+ ) ( 6 b-5 ) to get ( -3 a+2 b+3 ? ) A. ( 5+4 b-8 ) в. ( 5 a+4 b-8 ) c. ( 5 a+4 a b-8 ) D. ( 5 a+4 b-10 ) | 8 |
| 156 | State whether True or False. Multiply: ( x^{2}+x+1 ) by ( 1-x ) The answer is ( 1-x^{3} ) A. True B. False | 8 |
| 157 | ( x^{3}-x-4 ) added to ( x^{4}-x^{3}-x^{2}+ ) ( x+3 ) to obtain ( x^{4}+x^{2}-1 ? ) If true then enter 1 and if false then enter ( mathbf{0} ) | 8 |
| 158 | ( left(x^{3}+x^{2}-3 x+5right)+(x-1) ) | 8 |
| 159 | If ( frac{x^{2}+1}{x}=3 frac{1}{3} ) and ( x>1 ; ) find the value of ( x-frac{1}{x} ) A ( cdot 2 frac{2}{3} ) в. ( 1 frac{2}{9} ) c. ( 2 frac{5}{7} ) D. ( 1 frac{1}{3} ) | 8 |
| 160 | Add ( -7 m n+5,12 m n+2,9 m n- ) ( 8,-2 m n-3 ) | 8 |
| 161 | ( left(x^{2}+y^{2}-z^{2}right)^{2}-left(x^{2}-y^{2}+z^{2}right)^{2}= ) ( A cdot O ) B ( cdot 4 x^{2} z^{2} y^{2} ) C ( .-4 x^{2} z^{2}+4 x^{2} y^{2} ) D・ ( x^{4}+y^{4}+z^{4} ) | 8 |
| 162 | Simplify the polynomial and write it in standard form: ( left(x^{4}-3right)(3 x-4)+2 x^{3}left(2 x^{2}-2right) ) | 8 |
| 163 | If both ( x+1 ) and ( x-1 ) are factors of ( a x^{3}+ ) ( x^{2}-2 x+b, ) find the values of a and ( b ) | 8 |
| 164 | The product of ( frac{2}{3} x y ) and ( frac{3}{2} x z ) is equal to A ( cdot frac{1}{6} x y z ) в. ( x^{2} y z ) c. ( 6 x^{2} y z ) D. none of these | 8 |
| 165 | Subtract ( : frac{3}{2} x^{2} y+frac{4}{5} y-frac{1}{3} x^{2} y z ) from ( frac{3}{5} x y z-frac{2}{3} x^{2} y ) | 8 |
| 166 | Using ( (boldsymbol{x}+boldsymbol{a})(boldsymbol{x}+boldsymbol{b})=boldsymbol{x}^{2}+(boldsymbol{a}+ ) ( b) x+a b, ) find ( 12.1^{2}-7.9^{2} ) A . 97 B. 65 ( c cdot 34 ) ( D cdot 84 ) | 8 |
| 167 | From ( 8-y+2 y^{2} ) take away ( left(y^{2}-7-2 yright) ) A ( cdot y^{2}+y+15 ) B. ( 5 y^{2}-1 ) c. ( 3 y-7 y^{2}+11 ) D. None of these | 8 |
| 168 | Subtract the second expression from the first expression ( 5 x^{2}+3 x y+7 y^{2}, 3 x^{2}+x y+2 y^{2} ) | 8 |
| 169 | Add: ( -7 m n+5,12 m n+2,8 m n-8,-2 m n-3 ) | 8 |
| 170 | Simplify the expression ( left(2 x^{4}-5 x^{4}right)^{2} ) and choose the correct option. A . ( -21 x^{8} ) В. ( -6 x^{8} ) ( mathrm{c} cdot 9 x^{8} ) D. ( 9 x^{16} ) | 8 |
| 171 | ( operatorname{Let} g(x)=x^{6}+a x^{5}+b x^{4}+c^{3}+d x^{2} ) ( boldsymbol{g}(mathbf{1})=mathbf{1}, boldsymbol{g}(mathbf{2})=mathbf{2}, boldsymbol{g}(mathbf{3})=mathbf{3}, boldsymbol{g}(mathbf{4})=mathbf{4} ) A . zero B. c. 10 D. 727 | 8 |
| 172 | State True or False: On subtracting ( -3 x^{3}+4 x^{2}-5 x+6 ) from ( 3 x^{3}-4 x^{2}+5 x-6, ) the answer is ( 6 x^{3}-8 x^{2}+10 x-12 ) A. True B. False | 8 |
| 173 | If ( p(x)=x^{2}-4, q(x)=x^{3}-8, r(x)= ) ( (x+2) ) and ( s(x)=left(x^{2}+2 x+4right) ) then choose the correct options – A ( cdot p(x) cdot s(x)=q(x) cdot r(x) ) B . ( p(x) . s(x) neq q(x) . r(x) ) c. ( p(x) . q(x)=s(x) . r(x) ) D. None of these | 8 |
| 174 | Multiply ( left(3 p-q^{2}right)left(7 q+4 p^{4}right) ) | 8 |
| 175 | Obtain the product of: ( r n,-m n, m n p ) A ( .-m^{3} n^{3} p ) В. ( -m^{2} n^{2} p ) c. ( m^{2} n^{2} p ) D. ( -m^{3} n^{2} p ) | 8 |
| 176 | State whether the statement is True or False. ( (4+5 x)(4-5 x) ) is equal to ( 16-25 x^{2} ) A. True B. False | 8 |
| 177 | Find the product of the following pair of monomial. ( 4 p^{3},-3 p ) | 8 |
| 178 | Find the product of the following: ( (1+x)left(1-x+x^{2}right) ) | 8 |
| 179 | What is the result when ( 2 x^{2}+5 x-6 ) is subtracted from ( 4 x^{2}-9 x+6 ) | 8 |
| 180 | Simplify ( left(x^{2}-5right)(x+5)+25 ) A ( cdot x^{2}(x+5)-5(x+5)+15 ) B . ( x^{2}(x+5)-5(x-5)+25 ) c. ( x^{2}(x+5)-5(x+5)+25 ) D. ( x^{2}(x+5)-(x+5)+25 ) | 8 |
| 181 | ( (p+q)-(p-q) ) is equal to ( mathbf{A} cdot 2 p+2 q ) в. ( 2 p ) c. ( 2 q ) D. 0 | 8 |
| 182 | Simplify ( (2 a+b)(c-2 d)+(a- ) ( boldsymbol{b})(boldsymbol{2} boldsymbol{c}+boldsymbol{3} boldsymbol{d})+boldsymbol{4}(boldsymbol{a} boldsymbol{c}+boldsymbol{b} boldsymbol{d}) ) A. ( 8 a d+a c b-c-b d ) B. ( 8 a c-a d-b c-b d ) c. ( 8 c-a d+b c-d ) D. ( 8 a c+a d-b c d ) | 8 |
| 183 | What should be subtracted from ( 2 a^{2}- ) ( b^{2}+3 a^{2} b ) to get ( a^{2}+b^{2}+3 a b^{2}-6 ? ) | 8 |
| 184 | Simplify: ( (p q-q r+p r)(p q+q r)-(p r+ ) ( boldsymbol{p q}(boldsymbol{p}+boldsymbol{q}-boldsymbol{r}) ) | 8 |
| 185 | Multiply ( (5-2 x) ) and ( (3+x) ) A. ( 15-x+2 x^{2} ) B . ( 15-x-x^{2} ) c. ( 15-x-2 x^{2} ) D. ( 15-x+x^{2} ) | 8 |
| 186 | The product of ( left(3 x^{2}-5 x+6right) ) and ( -8 x^{3} ) when ( x=0 ) is A ( cdot frac{1}{2} ) B . 2 ( c cdot 1 ) D. | 8 |
| 187 | Simplify ( 3 x^{2}+5 x y-4 y^{2}+x^{2}- ) ( 8 x y-5 y^{2} ) | 8 |
| 188 | 11. Find the value of 1002-992. | 8 |
| 189 | Simplify the following expression. ( 6 x y+13 x-2 y x-5 x ) | 8 |
Hope you will like above questions on algebraic expressions and identities and follow us on social network to get more knowledge with us. If you have any question or answer on above algebraic expressions and identities questions, comments us in comment box.
Stay in touch. Ask Questions.
Lean on us for help, strategies and expertise.
