Algebraic Expressions And Identities Questions

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Algebraic Expressions And Identities Questions

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
5Add 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
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
74Add the followign:
( 13 x^{2},-31 x^{2}, 25 x^{2} )
8
75Add the following expressions:
( 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
130Add the following
(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
169Add:
( -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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