Question
Factorise:
$125-8 x^3-27 y^3-90 x y$
$125-8 x^3-27 y^3-90 x y$
✓
Answer
$125-8 x^3-27 y^3-90 x y$
$=5^3+(-2 x)^3+(-3 y)^3-3 \times 5 \times(-2 x) \times(-3 y)$
$=[5+(-2 x)+(-3 y)]\left[5^2+(-2 x)^2+(-3 y)^2-5 \times(-2 x)-(-2 x)(-3 y)-5 \times(-3 y)\right]$
$=(5-2 x-3 y)\left(25+4 x^2+9 y^2+10 x-6 x y+15 y\right)$
$=5^3+(-2 x)^3+(-3 y)^3-3 \times 5 \times(-2 x) \times(-3 y)$
$=[5+(-2 x)+(-3 y)]\left[5^2+(-2 x)^2+(-3 y)^2-5 \times(-2 x)-(-2 x)(-3 y)-5 \times(-3 y)\right]$
$=(5-2 x-3 y)\left(25+4 x^2+9 y^2+10 x-6 x y+15 y\right)$
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