Question

factorize (x+y)^3-(x-y)^3​

Answer 1

Answer :-

2y(3x² + y²)

Solution :-

(x + y)³ - (x - y)³

We know that

a³ - b³ = (a - b)(a² + ab + b³

Here

• a = x + y

• b = x - y

By substituting the values in the RHS of the identity

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

= (x + y - x + y){x² + y² + 2xy + (x² - y²) + (x² + y² - 2xy)}

[ Identities used :-

• (x + y)² = x² + y² + 2xy

• (x - y)² = x² + y² - 2xy

• (x + y)(x - y) = x² - y² ]

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

= 2y(3x² + y²)