Question
Factorize:
$8x^3 + 27y^3 + 36x^2y + 54xy^2$
$8x^3 + 27y^3 + 36x^2y + 54xy^2$
✓
Answer
$8 x^3+27 y^3+36 x^2 y+54 x y^2$
$=(2 x)^3+(3 y)^3+3 \times(2 x)^2 \times 3 y+3 \times(2 x)(3 y)^2$
$=(2 x+3 y)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
$\therefore 8 x^3+27 y^3+36 x^2 y+54 x y^2$
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
$=(2 x)^3+(3 y)^3+3 \times(2 x)^2 \times 3 y+3 \times(2 x)(3 y)^2$
$=(2 x+3 y)^3\left[\because a^3+b^3+3 a^2 b+3 a b^2=(a+b)^3\right]$
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
$\therefore 8 x^3+27 y^3+36 x^2 y+54 x y^2$
$=(2 x+3 y)(2 x+3 y)(2 x+3 y)$
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