Algebraic Expressions And Identities Questions

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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

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