Question

Prove that : (x + y)3 - (x - y)3 – 6y (x2 - y2) =8y3​

Answer 1

see in the attachment .

Answer 2

$\boxed{\Huge\mathfrak{ANSWER}}$

$(x+y)^3 - (x-y)^3 -6y(x^2-y^2)=8y^3$

$\implies x^3+3x^2y+3xy^2+y^3-( x^3-3x^2y+3xy^2-y^3)-6x^2y+6y^3=8y^3$

$\implies 3x^2y+y^3+3x^2y+y^3-6x^2y+6y^3=8y^3$

$\implies 6x^2y+2y^3-6x^2y+6y^3=8y^3$

$Now\;6x^2y \;cancels\; out$,

$\implies 2y^3+6y^3=8y^3$

$\implies 8y^3=8y^3(proved)$