Question
Factorize:
$x^3 + 8y^3 + 6x^2y + 12xy^2$
$x^3 + 8y^3 + 6x^2y + 12xy^2$
✓
Answer
$x^3+8 y^3+6 x^2 y+12 x y^2$
$=(x)^3+(2 y)^3+3 \times x^2 \times 2 y+3 \times x \times(2 y)^2$
$=(x+2 y)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(x+2 y)(x+2 y)(x+2 y)$
$\therefore x^3+8 y^3+6 x^2 y+12 x y^2$
$=(x+2 y)(x+2 y)(x+2 y)$
$=(x)^3+(2 y)^3+3 \times x^2 \times 2 y+3 \times x \times(2 y)^2$
$=(x+2 y)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(x+2 y)(x+2 y)(x+2 y)$
$\therefore x^3+8 y^3+6 x^2 y+12 x y^2$
$=(x+2 y)(x+2 y)(x+2 y)$
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