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