Question

factorize
(i)27x³-8y³
(ii)64x³+343y³
(iii)64x³-343y³​

Answer 1

Step-by-step explanation:

$i) {27x}^{3} - {8y}^{3} \\ use \: identity \: {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )\\ = {(3x)}^{3} - {(2y)}^{3} \\ = (3x - 2y)( 9 {x}^{2} + (3x)(2y) + 4 {y}^{2} ) \\ = (3x - 2y)( 9 {x}^{2} + 6xy + 4 {y}^{2} )$

Answers to the next questions is given in attachments.

Answer 2

Answer :-

(i) (3x - 2y)(9x² + 6xy + 4y²)

(ii) (4x + 7y)(16x² - 28xy + 49y²)

(iii) (4x - 7y)(16x² + 28xy + 49y²)

Solution :-

(i) 27x³ - 8y³

It can be written as

= (3x)³ - (2y)³

We know that

a³ - b³ = (a - b)(a² + ab + b²)

Here

• a = 3x

• b = 2y

By substituting the values

= (3x - 2y){(3x)² + 3x(2y) + (2y)²}

= (3x - 2y)(9x² + 6xy + 4y²)

(ii) 64x³ + 343y³

It can be written as

= (4x)³ + (7y)³

We know that

a³ + b³ = (a + b)(a² - ab + b²)

Here

• a = 4x

• b = 7y

By substituting the values

= (4x + 7y){(4x)² - 4x(7y) + (7y)²}

= (4x + 7y)(16x² - 28xy + 49y²)

(iii) 64³ - 343y³

It can be written as

= (4x)³ - (7y)³

We know that

a³ - b³ = (a - b)(a² + ab + b²)

Here

• a = 4x

• b = 7y

By substituting the values

= (4x - 7y){(4x)² + 4x(7y) + (7y)²}

= (4x - 7y)(16x² + 28xy + 49y²)