Question
Factorise the following:$x^3y^3 - 8x^2y^2 + 15xy$
✓
Answer
$x^3y^3 - 8x^2y^2 + 15xy$
$= x^3y^3 - 3x^2y^2 - 5x^2y^2 + 15xy$
$= x^2y^2(xy - 3) - 5xy(xy - 3)$
$= (xy - 3)(x^2y^2 - 5xy)$
$= (xy - 3)xy(xy - 5)$
$= xy(xy - 3)(xy - 5).$
$= x^3y^3 - 3x^2y^2 - 5x^2y^2 + 15xy$
$= x^2y^2(xy - 3) - 5xy(xy - 3)$
$= (xy - 3)(x^2y^2 - 5xy)$
$= (xy - 3)xy(xy - 5)$
$= xy(xy - 3)(xy - 5).$
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