Test: Algebraic Identities Cubic Type


20 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Algebraic Identities Cubic Type


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QUESTION: 1

Expansion and simplification of 8(3h - 4) + 5(h - 2) gives

Solution:

Now, 8 (3h - 4) + 5 (h - 2)

= 24h - 32 + 5h - 10, the expansion

= 24h + 5h - 32 - 10

= 29h - 42, the simplification

QUESTION: 2

Evaluate (11)3

Solution:

11³= (10+1)³=1000+1+30(11)=1001+330=1331

QUESTION: 3

Factorise:(3x- 5y)3+ (5y – 2z)3 + (2z – 3x)3

Solution:
QUESTION: 4

Evaluate: 53 – 23 – 33

Solution:

53 - 23 - 33​​​​​​​
= 125 - 8 - 27
= 90

QUESTION: 5

Factorise : 8a3+ b3 + 12a2b + 6a b2

Solution:

8a3 + b3+ 12a2b + 6ab2
8a3 + b3+ 12a2b + 6ab2
= (2a)3 + (b)3 + 3(2a)(b) (2a + b)
= (2a + b)3 | Using Identity VI
= (2a + b)(2a + b)(2a + b)

QUESTION: 6

Evaluate (x+y+z)2

Solution:
QUESTION: 7

Factorise : 8a3 + b3 + 12a2 b + 6ab2

Solution:

8a3 + b3+ 12a2b + 6ab2
8a3 + b3+ 12a2b + 6ab2
= (2a)3 + (b)3 + 3(2a)(b) (2a + b)
= (2a + b)3 | Using Identity VI
= (2a + b)(2a + b)(2a + b)

QUESTION: 8

p3+ q3 + r3 – 3pqr = ?​

Solution:
QUESTION: 9

Factorize: 125a3 – 27b3 – 225a2b + 135ab2.​

Solution:
QUESTION: 10

Evaluate (104)3

Solution:

(104)³ 
=(100 + 4)³ 
Use ( a +b)³ = a³ + b³ + 3ab( a + b)
then,
( 100 + 4)³ = ( 100)³ +(4)³ +3(100)(4)(100+4)
=(10²)³ + 64 + 1200(104)
=1000000 + 64 + 124800
=1124864.

QUESTION: 11

Factorize: (x – y)3 + (y – z)3 + (z – x)3

Solution:
QUESTION: 12

Factorise: x7y + xy7

Solution:
QUESTION: 13

What is the value 83 – 33 (without solving the cubes)?​

Solution:

(8-3)((8)² + 8×3 + (3)²) = 5(64 + 24 + 9) = 5×97 = 485

QUESTION: 14

p3+ q3 = ?​

Solution:
QUESTION: 15

What is the value of 53 – 13(without solving cube)?

Solution:

53 - 13 can be solved using the identity ;

(a3 - b3) = (a - b) (a2 + b2 + ab)

53 - 13 = ( 5 - 1 ) ( 52 + 12 + 5*1)

=(4) (25 + 1 + 5)

= (4) (31)

= 124

QUESTION: 16

Factorize: 27x3 – 125y3

Solution:
QUESTION: 17

a3 – b3 equals​

Solution:

It is the identity equation

In the fraction equation

QUESTION: 18

Evaluate: 303 + 203 – 503.​

Solution:

We have to find the value of

QUESTION: 19

If  , the value of x3 – y3 is :

Solution:
QUESTION: 20

Factorization of 103²-9 yields

Solution: