Question
Factorize the following expressions:
$125+8 x^3-27 y^3+90 x y$
$125+8 x^3-27 y^3+90 x y$
✓
Answer
$125+8 x^3-27 y^3+90 x y$
$=5^3+(2 x)^3+(-3 y)^3-3 \times 5 \times 2 x \times(-3 y)$
$=(5+2 x+(-3 y))\left(5^2+(2 x)^2+(-3 y)^2-5(2 x)-2 x(-3 y)-(-3 y) 5\right)$
$=(5+2 x+-3 y)\left(25+4 x^2+9 y^2-10 x+6 x y+15 y\right)$
$\therefore 125+8 x^3-27 y^3+90 x y$
$=(5+2 x+-3 y)\left(25+4 x^2+9 y^2-10 x+6 x y+15 y\right)$
$=5^3+(2 x)^3+(-3 y)^3-3 \times 5 \times 2 x \times(-3 y)$
$=(5+2 x+(-3 y))\left(5^2+(2 x)^2+(-3 y)^2-5(2 x)-2 x(-3 y)-(-3 y) 5\right)$
$=(5+2 x+-3 y)\left(25+4 x^2+9 y^2-10 x+6 x y+15 y\right)$
$\therefore 125+8 x^3-27 y^3+90 x y$
$=(5+2 x+-3 y)\left(25+4 x^2+9 y^2-10 x+6 x y+15 y\right)$
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