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Published on: 07/09/2019
Algebraic Expressions and Identities
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Questions + Answers key
Take MCQ Mathematics Test
1.
Solve the following using identities.104\(\times\)97
2.
Solve the following using identities.47\(\times\)53
3.
Simplify (3x + 2y)2 + (3x- 2y)2.
4.
Show that a2 + 3a+ 2= 132 is not true for a=-5 and for a= 0.
5.
Write two like terms of the following
7xy
6.
Express the following product as a monomial \(\left( { a }^{ 4 } \right) \times \left( { 2a }^{ 3 } \right) \times \left( \frac { 1 }{ 5 } { a }^{ 2 } \right) \times \left( -5a \right) \)
7.
Obtain the product of m, - mn,mnp
8.
Find the product of the following pairs of monomials - 4p,7p
9.
Add the following 2p2q2 - 3pq + 4,5 + 7pq - 3p2q2
10.
Identify the terms, their coefficients for each of the following expressions,
3- pq+ qr- rp
11.
Product of the monomials, -15p, -13q2, pq is
-165p2q3
195p2q3
195p3q2
-195p3q2
12.
Area of a rectangle with length 5ab and breadth 13ac2 is
65a2bc
35a2bc2
65a2bc2
65abc2
13.
Sum of a - b + ab, b + c - bc and c - a - ac is
ab-2c+ac-bc
2c-ab-ac-bc
2c+ab-ac-bc
2c-ab+ac-bc
14.
Which of the following is a binomial?
13xb+b
6b2+7a+2c
45(b2+ a)
13ax3bx5c
15.
Which of the following is an identity?
(b+c)=b2+c2
b2-c2=(b+c)2-4bc
b2-c2 =(b-c)2
(b+ c)2 =b2 + 2bc+c2
16.
On subtracting -3a2b2 from a2b2, we get_______
17.
The sum of 13pq2 and -7q2p is_______
18.
The product of two terms with unlike signs is a______________term
19.
The product of two terms with like signs is a__________term
20.
Square of (3a+5b) is________
21.
The product of 24xyz2 and 3xy2 is 72x2y3z2. Match the Columns
22.
Like term as 15a3b2 is 25a3b2c.
23.
Sum of 16a2bc, - 8b2ac and 8a2bc is 16a2bc.
24.
The difference of the squares of two consecutive numbers is their sum
25.
The value of (a + b)2 + (a - b)2 is 4ab.
26.
One day, Sahil went to playa cricket tournament (organised in a sports complex) along with his two friends Rahul and Sunil. Someone stole Sahil's bicycle but Rahul and Sunil helped him to buy a new one bicycle contributing rs(2x +80) and rs (8x + 20), respectively, If the bicycle costs rs. 2100,
(a) what were the amount given by Rahul and Sunil to Sahil?
(b) what are the values depicted by Rahul and Sunil here?
27.
If 2x + 3y =5 and xy =1, then find the value of 4x2 + 9y2.
1.
10088
2.
2491
3.
(3x + 2y)2 =(3x)2 + (2y)2 + 2 x(3x)(2y)
= 9x2 + 4y2 + 12xy
Similarly, (3x - 2y)2 = 9x2 + 4y2 -12xy
(3x + 2y)2 + (3x - 2y)2
= (9x2 + 4y2 + 12xy) + (9x2 + 4y2 -12xy)
=18x2+8y2
4.
For a = - 5,
LHS = a2 + 3a + 2
=(-5)2+3x(-5)+2=25-15+2=12
and RHS =132
\(\because LHS\neq RHS\)
So, it is not true for a = - 5
For a =0,
LHS = a2 + 3a + 2
= (0)2 + 3 x 0 + 2 = 0 + 0 + 2 = 2
and RHS =132
\(\because LHS\neq RHS\)
So, it is not true for a = 0.
5.
14xy,21xy
6.
-2a10
7.
Required product = - m3 n2p
8.
we have,-4p,7p
(-4p) x (7p) = {(-4) x 7} x (p x p)
= (-28) x p2 = - 28p2
9.
2p2q2 - 3pq + 4
-3p2q2 + 7pq + 5
\(\overline { \underline { -{ p }^{ 2 }{ q }^{ 2 }+4pq+9 } } \)
10.
We have, 3 - pq + qr - rp
| Terms | 3 | -pq | qr | -rp |
| Coefficients | 3 | -1 | 1 | -1 |
11.
(b)
195p2q3
12.
(c)
65a2bc2
13.
(c)
2c+ab-ac-bc
14.
(c)
45(b2+ a)
15.
(d)
(b+ c)2 =b2 + 2bc+c2
16.
( )
\(\because\) a2b2-(-3a2b2)=a2b2+3a2b2=4a2b2
17.
( )
\(\because\) 13pq2-7q2p=6pq2
18.
( )
(-a)\(\times \)a2=-a3 and (-ab)\(\times \)(b2)=-ab3ââââââââââââââ
19.
( )
(-a)\(\times \)(-a)2=a3 and (ab)\(\times \)(b2)=ab3âââââââ
20.
( )
âĩ(3a+5)2=(3a)2+2.(3a).(5b)+(5b)2=9a2+30ab+25b2
21.
(a)
22.
(b)
23.
(b)
24.
(a)
25.
(b)
26.
(a) Rahul contributed =rs(2x + 80)
Sunil contributed = rs(8x + 20)
The total amount=rs[(2x+80)+(8x+20)]
=2100
2x + 8x + 80+ 20 = 2100
10x=2000
x=200
Thus, Rahul's contribution
= 2x + 80= 2 x 200 + 80
= 400 + 80= rs480
and Sunil's contributuib
= 8x + 20 = 8 x 200 + 20
= 1600 + 20 = rs1620
Thus, Rahul's and Sunil contributed rs480 and rs1620 respectively
(b) Rahul and Sunil are very cooperative by nature and they literally proved that "A friend in need is a friend indeed".
27.
13
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