# Algebraic Expressions And Identities Questions

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 NoQuestionsClass
1Simplify: ( (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
2Subtract 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
3Simplify ( 2(3 b-5 a)-7[9- )
( 62-5(a-6)] )
8
4What 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
(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
6Expand 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
8Simplify: ( sqrt{boldsymbol{x}^{2}}+sqrt{boldsymbol{y}^{2}}-boldsymbol{x}-boldsymbol{y}+ )
( sqrt{(boldsymbol{a}+boldsymbol{b})^{2}} )
8
9How much is ( x+3 y-4 z ) greater than ( 3 x-2 y+z ? )8
10Subtract :
( -x^{2}+y^{2}-x^{2} y+5 x y^{2} ) from ( x^{2}+ )
( x^{2} y-5 x y^{2}-y^{2} )
8
11Simplify: ( 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
12Addition of ( left(x^{2}+y^{2}right) ) and ( left(x^{2}-y^{2}right) )
is
8
1369.
If a + b2 + c = ab + bc + ca,
a
+ c
is
then the value of h
(1) 3
(2) 2
(3) o
(4) 1
8
14Add: ( 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
15Solve :
( left(x^{2}+4 x yright)+left(4 y^{2}-9 z^{2}right) )
8
16If ( 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
17State 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
18Simplify
( 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
19Simplify the polynomial and write it in
standard form:
( (-2 x-5)(2 x-8)-(2 x-5)(3 x+7) )
8
2065. 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
21Factorise :
( z^{2}-left(x^{2}-2 x y+y^{2}right) )
8
22What should be added to ( x^{2}+x y+y^{2} )
to obtain ( 2 x^{2}+3 x y ? )
8
23If ( 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
24Solve ( left(boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1}right)left(boldsymbol{x}^{4}+boldsymbol{x}^{3}+boldsymbol{x}+mathbf{1}right) )8
25Solve
( left(3 x^{2}+4 yright) times(2 x+3 y) )
8
26State 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
27Subtract ( 5 x y ) from ( 8 x y )8
28Find the constant after subtracting from ( x^{4}+4 x^{2}-3 x+7 ) to get ( 3 x^{3}- )
( x^{2}+2 x+1 ? )
8
29Subtract ( 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
30If ( 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 identity8
32Find 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
33Add all of them ( x-8 y, 3 x y-y ) and
( boldsymbol{y}+mathbf{1} )
8
34Show 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
35If ( 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
36Subtract ( 24 a b-10 b-18 a ) from
( 30 a b+12 b+14 a )
8
37Which 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
3951. 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
40Simplify combining like terms. ( 21 b-32+7 b-20 b )8
41Add 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
42From the sum of ( 3 x-y+11 ) and ( -y- )
11 subtract ( 3 x-y-11 )
8
43What 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
44What 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
45State 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
46Simplify: ( (3.5 e-4.5 f)(1.5 e+4 f+ )
( e f)-4.5 e+10 f )
8
47Find 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
48Give expressions in the following cases.
( boldsymbol{y} ) is multiplied by 5 and results is subtracted from 16.
8
49Multiply:
( left(m^{2}-5right) timesleft(m^{3}+2 m-2right) )
8
50select 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
51Find 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
52Substract ( x^{2} ) from ( x^{2}+y^{2}-3 y )8
53How 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
54Evaluate: ( left(4 x^{2}-frac{1}{5} x+7right)- )
( left(-2 x^{2}-frac{1}{2} x+frac{1}{3}right) )
8
55Subtract.
( 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
57By how much does ( x^{2}-2 a x+5 ) exceed
( 3 x^{2}-5 x+6 ? )
8
58Simplify 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
59Find 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
60Simplify: ( 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
61Simplify:
( 25 a b c^{2}-15 a^{2} b^{2} c )
8
62Evaluate: ( (l+m)-4 m )8
63Add 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
64The length and breadth and height of a cuboid are ( (x+3),(x-2) ) and ( (x-1) )
respectively. Find its volume.
8
65Which 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
66Add ( 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
67Add ( a+b-3, b-a+3, a-b+3 )8
68Simplify :
( x y+left(x y+4 x^{3}+3 x-5right)-left(-3 x^{2}-right. )
4) ( -left(x y+x^{3}-4right) )
8
69State 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
71If ( 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
72State True or False
( 13 m^{2}-2 m^{2}=11 m^{2} )
A. True
B. False
8
73Subtract the second expression from the first expression
( boldsymbol{x}+mathbf{2} boldsymbol{y}+boldsymbol{z},-boldsymbol{x}-boldsymbol{y}-mathbf{3} boldsymbol{z} )
8
( 13 x^{2},-31 x^{2}, 25 x^{2} )
8
( boldsymbol{a}+boldsymbol{b}-mathbf{3}, boldsymbol{b}-boldsymbol{a}+mathbf{3}, boldsymbol{a}-boldsymbol{b}+mathbf{3} )
8
76Simplify: ( 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
77Simplify:
( (2 p+3 q+4 r)(9 p-r)+(p+q+r) )
8
78Add ( 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
79Simplify
( (a+b)(c-d)+(a-b)(c+d) )
8
80Form 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
81Add: ( a+b+a b ; b-c+b c ) and ( c+ )
( a+a c )
8
82Find 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
83Simplify 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
85Multiply: ( 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
86Prove that:
( frac{1}{1+x^{a-b}}+frac{1}{1+x^{b-a}}=1 )
8
87Find the value of the addition of ( (x- ) ( 3 y+4 z),(y-2 x-8 z),(5 x-2 y- )
( 3 z) )
8
8862. 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
90Find 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
92State 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
93Multiply: ( (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
94Evaluate ( a^{2}-b^{2}-(a+b)^{2} )8
95Find 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
96In 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
97What 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
98Find each of the following products.
( 6 a times 4 b^{2} )
8
99Simplify:
( 4(x-5) )
A ( .4 x-5 )
B. ( 4 x-20 )
c. ( 4 x+5 )
D. ( 4 x+20 )
8
100If ( 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
101From 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
102Subtract ( 3 x y+2 z^{2} ) from ( 5 x y+3 z^{2}- )
( x z )
8
103Simplify ( (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
104Evaluate:
( 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
105The 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
106The 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
109Give expressions in the following cases. 11 added to ( 2 m )8
110Subtract: ( a(b-5) ) from ( b(5-a) )8
111Simplify: ( y(x-2 y)^{2}-13+4(x-1) )8
112What 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
113Simplify 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
114By how much does ( 3 x-4 x y+2 z ) exceed ( 8 x+5 z-7 x y ? )8
115Solve:
Add ( 3 a(a-b+c), 2 b(a-b+c) )
8
116What 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
117Simplify :
( 3 a-2 b-a b-(a-b+a b)+3 a b+ )
( boldsymbol{b}-boldsymbol{a} )
8
118Simplify: ( (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
119Subtract 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
120solve ( boldsymbol{a}^{boldsymbol{7}}+frac{mathbf{1}}{boldsymbol{a}^{boldsymbol{9}}}=? )8
121Solve: ( frac{boldsymbol{x}+mathbf{2 0}}{mathbf{9}}+frac{mathbf{3} boldsymbol{x}}{mathbf{7}}=mathbf{6} )8
122Add 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
125How much does ( -5 a^{2}+3 a-5 b^{2} )
( operatorname{exceed} 7 a^{2}+4 a-9 b^{2} ? )
8
126Which 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
127Find the joint equation of the following pair of lines. ( x+2 y-1=0 ) and ( 2 x-3 y+2=0 )8
128Simplify ( left(5 p^{2}-3right)+left(2 p^{2}-3 p^{3}right) )8
129Factorize ( left(1+frac{1}{x}+frac{1}{x^{2}}+frac{1}{x^{3}}right) )8
(i) ( x-3 y-2 z )
( 5 x+7 y-8 z )
( 3 x-2 y+5 z )
8
131Subtract:
( a+2 b-c ) from ( 3 a-b+2 c )
8
132Factorize:
( 16 a^{4}-9 b^{4} )
8
133Simplify
( 12-left(x+x^{2}right)left(8-x-x^{2}right) )
8
134What 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
135Subtract ( 4 a b c ) from ( -6 a b c )8
136Find 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
137Simplify 🙁 x^{2}+z^{2}-2 x z )8
138Subtract 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
139Find the ( left[frac{7}{9} p^{2} q rright] timesleft(18 p q^{2}right)left(-frac{3}{14} r^{2}right) )8
140Let 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
141State 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
142Multiply:
( -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
143Subtract 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
144If ( 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
145What should be added to ( x^{2}+x y+y^{2} )
to obtain ( 2 x^{2}+3 x y )
8
146Given 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
147Simpllify ( : 2 x^{2}+5 x-1+8 x+x^{2}+ )
( 7-6 x+3-3 x^{2} )
8
148Simplify combining like terms:
( left(3 y^{2}+5 y-4right)-left(8 y-y^{2}-4right) )
8
149The 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
150Evaluate: ( 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
151Find 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
152Simplify: ( boldsymbol{x}+mathbf{2} boldsymbol{x}+mathbf{3} boldsymbol{x} )
( mathbf{A} cdot mathbf{5} )
B. ( 5 x )
( c .6 )
D. ( 6 x )
8
153Evaluate
( 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
155What 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
156State 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
159If ( 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
160Add ( -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
162Simplify the polynomial and write it in standard form:
( left(x^{4}-3right)(3 x-4)+2 x^{3}left(2 x^{2}-2right) )
8
163If 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
164The 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
165Subtract ( : 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
166Using ( (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
167From ( 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
168Subtract 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
( -7 m n+5,12 m n+2,8 m n-8,-2 m n-3 )
8
170Simplify 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
172State 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
173If ( 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
174Multiply ( left(3 p-q^{2}right)left(7 q+4 p^{4}right) )8
175Obtain 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
176State 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
177Find the product of the following pair of monomial.
( 4 p^{3},-3 p )
8
178Find the product of the following:
( (1+x)left(1-x+x^{2}right) )
8
179What is the result when ( 2 x^{2}+5 x-6 ) is
subtracted from ( 4 x^{2}-9 x+6 )
8
180Simplify ( 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
182Simplify ( (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
183What 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
184Simplify:
( (p q-q r+p r)(p q+q r)-(p r+ )
( boldsymbol{p q}(boldsymbol{p}+boldsymbol{q}-boldsymbol{r}) )
8
185Multiply ( (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
186The 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
187Simplify ( 3 x^{2}+5 x y-4 y^{2}+x^{2}- )
( 8 x y-5 y^{2} )
8
18811.
Find the value of 1002-992.
8
189Simplify the following expression.
( 6 x y+13 x-2 y x-5 x )
8

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