Question

x3-y3=(x-y)(x2+xy+y2)​

Answer 1

RHS = (x-y)(x²+xy+y²)

= x(x²+xy+y²)-y(x²+xy+y²)

= x³+x²y+xy²-x²y-xy²-y³

After cancellation,we get

= x³-y³

= LHS

Therefore,

x³-y³ = (x-y)(x²+xy+y²)

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Right Hand Side = (x - y)(x² + xy + y²)

Factorize in the meaningful way

= x(x² + xy + y²) - y(x² + xy + y²)

= x³ + x²y + xy² -x²y - xy² - y³

= x³-y³                 [Proved]

⇒ x³ - y³ = (x - y) (x² + xy + y²)

$\bf\huge\bf\huge{\boxed{\bigstar{{LHS = RHS}}}}$