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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: 5^{3} – 2^{3} – 3^{3}

Solution:

5^{3} - 2^{3} - 3^{3}

= 125 - 8 - 27

= 90

QUESTION: 5

Factorise : 8a^{3}+ b^{3} + 12a^{2}b + 6a b^{2}

Solution:

8a^{3} + b^{3}+ 12a^{2}b + 6ab^{2}

8a^{3} + b^{3}+ 12a^{2}b + 6ab^{2}

= (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 : 8a^{3} + b^{3} + 12a^{2} b + 6ab^{2}

Solution:

8a^{3} + b^{3}+ 12a^{2}b + 6ab^{2}

8a^{3} + b^{3}+ 12a^{2}b + 6ab^{2}

= (2a)^{3} + (b)^{3} + 3(2a)(b) (2a + b)

= (2a + b)^{3} | Using Identity VI

= (2a + b)(2a + b)(2a + b)

QUESTION: 8

p^{3}+ q^{3} + r^{3} – 3pqr = ?

Solution:

QUESTION: 9

Factorize: 125a^{3} – 27b^{3} – 225a^{2}b + 135ab^{2}.

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: x^{7}y + xy^{7}

Solution:

QUESTION: 13

What is the value 8^{3} – 3^{3} (without solving the cubes)?

Solution:

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

QUESTION: 14

p^{3}+ q^{3} = ?

Solution:

QUESTION: 15

What is the value of 5^{3} – 1^{3}(without solving cube)?

Solution:

5^{3} - 1^{3 }can be solved using the identity ;

(a^{3} - b^{3}) = (a - b) (a^{2} + b^{2} + ab)

5^{3} - 1^{3} = ( 5 - 1 ) ( 5^{2} + 1^{2} + 5*1)

=(4) (25 + 1 + 5)

= (4) (31)

= 124

QUESTION: 16

Factorize: 27x^{3} – 125y^{3}

Solution:

QUESTION: 17

a^{3} – b^{3} equals

Solution:

It is the identity equation

In the fraction equation

QUESTION: 18

Evaluate: 30^{3} + 20^{3} – 50^{3}.

Solution:

We have to find the value of

QUESTION: 19

If , the value of x^{3} – y^{3} is :

Solution:

QUESTION: 20

Factorization of 103²-9 yields

Solution:

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