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