Question

$x^3+y^3=(x+y)(x^2-xy+y^2)$ prove this identity.

Answer 1

Given, $x^3+y^3=(x+y)(x^2-xy+y^2)$
First take R.H.S
$(x+y)(x^2-xy+y^2)$
To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.
$=$ $x.x^2-x^{2}y+x.y^2+y.x^2-x.y^2+y.y^2$
$=$ $x^3-x^{2}y+x{y}^2+x^{2}y-x{y}^2+y^3$
$=$ $x^3+y^3$
So, L.H.S = R.H.S
$x^3+y^3=x^3+y^3$
Hence, $x^3+y^3=(x+y)(x^2-xy+y^2)$ is derived.