Question

Factorise:(x-y)^3-8x^3​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer :-

(x + y){-(7x² + y² - 4xy)

Solution :-

(x - y)³ - 8x³

It can be written as

= (x - y)³ - (2x)³

We know that

a³ - b³ = (a - b)(a² + ab + b²)

Here

a = x - y

b = 2x

By substituting the values

= (x - y - 2x){(x - y)² + (x - y)2x + (2x)²}

= (x - y - 2x)(x² + y² - 2xy + 2x² - 2xy + 4x²)

[Because (x - y)² = x² + y² - 2xy]

Adding like terms

= (- x - y)(7x² + y² - 4xy)

= - (x + y)(7x² + y² - 4xy)

= (x + y){-(7x² + y² - 4xy)

= (x + y)(-7x² - y² + 4xy)

Identity used :-

° a³ - b³ = (a - b)(a² + ab + b²)

°  (x - y)² = x² + y² - 2xy