Question
Factorize the following expressions:
$8 x^3 y^3+27 a^3$
$8 x^3 y^3+27 a^3$
✓
Answer
$8 x^3 y^3+27 a^3$
$=(2 x y)^3+(3 a)^3$
$=(2 x y+3 a)\left((2 x y)^2-2 x y \times 3 a+(3 a)^2\right)$
$\therefore\left[a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]=(2 x y+3 a)\left(4 x^2 y^2-6 x y a+9 a^2\right)$
$\therefore 8 x^3 y^3+27 a^3=(2 x y+3 a)\left(4 x^2 y^2-6 x y a+9 a^2\right)$
$=(2 x y)^3+(3 a)^3$
$=(2 x y+3 a)\left((2 x y)^2-2 x y \times 3 a+(3 a)^2\right)$
$\therefore\left[a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]=(2 x y+3 a)\left(4 x^2 y^2-6 x y a+9 a^2\right)$
$\therefore 8 x^3 y^3+27 a^3=(2 x y+3 a)\left(4 x^2 y^2-6 x y a+9 a^2\right)$
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