Question

Question 9
Verify:
$\left(i\right)x^3+y^3=(x+y)(x^2-xy+y^2)\left(ii\right)x^3-y^3=(x-y)(x^2+xy+y^2)$

Answer 1

$\left(i\right)x^3+y^3[usingidentity{a}^3+b^3=(a+b\left)\right(a^2-ab+b^2\left)\right]=(x+y)(x^2-xy+y^2)R.H.S.=x(x^2-xy+y^2)+y(x^2-xy+y^2)=x^3-x^{2}y+x{y}^2+y{x}^2-x{y}^2+y^3=x^3+y^3=L.H.S$

$\left(ii\right)x^3-y^3[usingidentity{a}^3-b^3=(a-b\left)\right(a^2+ab+b^2\left)\right]=(x-y)(x^2+xy+y^2)R.H.S.=x(x^2+xy+y^2)-y(x^2+xy+y^2)=x^3+x^{2}y+x{y}^2-y{x}^2-x{y}^2-y^3=x^3-y^3=L.H.S.$