Question

verify x³-y³=(x-y) (x²+xy+y²)​

Answer 1

We have to prove that x³ - y³ = (x-y)(x² + xy + y²)

So, Let's take R. H. S and prove it equal to L.H. S.R. H.

S= (x-y)(x² + xy + y²)

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

= x³ + x²y + xy² -yx² -xy² - y³

$= {x}^{3} + x ^{2}y + x {y}^{2} - {x}^{2}y - x {y}^{2} - {y}^{3} \\ \\ = {x}^{3} - {y}^{3}$

L.H.S

$\rm{hence \: proved}$