Question
Factorize:
$125 x^3-27 y^3-225 x^2 y+135 x y^2$
$125 x^3-27 y^3-225 x^2 y+135 x y^2$
✓
Answer
$125 x^3-27 y^3-225 x^2 y+135 x y^2$
$=(5 x)^3-(3 y)^3-3 x(5 x)^2 \times 3 y+3 \times(5 x)(3 y)^2$
$=(5 x-3 y)^3\left[\because a^3-b^3-3 a^2 b+3 a b^2=(a-b)^3\right]$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
$\therefore 125 x^3-27 y^3-225 a^2 y+135 x y^2$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
$=(5 x)^3-(3 y)^3-3 x(5 x)^2 \times 3 y+3 \times(5 x)(3 y)^2$
$=(5 x-3 y)^3\left[\because a^3-b^3-3 a^2 b+3 a b^2=(a-b)^3\right]$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
$\therefore 125 x^3-27 y^3-225 a^2 y+135 x y^2$
$=(5 x-3 y)(5 x-3 y)(5 x-3 y)$
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