Question

Solve:
(i) $8x^3+y^3$
(ii) $16(x+y{)}^3-27$

Answer 1

(i) $8x^3+y^3=(2x{)}^3+y^3$ $(\because a^3+b^3=(a+b\left)\right(a^2-ab+b^2)$

$=(2x+y)\left(\right(2x{)}^2-\left(2x\right)y+y^2)$

$=(2x+y)(4x^2-2xy+y^2)$

(ii) $16(x+y{)}^3-27$

$=16[x^3+3x^{2}y+3y^{2}x+y^3]-27$

$=16x^3+8x^{2}y+48x{y}^2+16y^3-27$.