Factor x^3y^2-27y^2

$x^{3} y^{2} - 27 y^{2}$

Step 1

Factor $y^{2}$ out of $x^{3} y^{2} - 27 y^{2}$ .

Factor $y^{2}$ out of $x^{3} y^{2}$ .

$y^{2} x^{3} - 27 y^{2}$

Factor $y^{2}$ out of $- 27 y^{2}$ .

$y^{2} x^{3} + y^{2} \cdot - 27$

Factor $y^{2}$ out of $y^{2} x^{3} + y^{2} \cdot - 27$ .

$y^{2} (x^{3} - 27)$

Step 2

Rewrite $27$ as $3^{3}$ .

$y^{2} (x^{3} - 3^{3})$

Step 3

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = 3$ .

$y^{2} ((x - 3) (x^{2} + x \cdot 3 + 3^{2}))$

Step 4

Factor.

Simplify.

Move $3$ to the left of $x$ .

$y^{2} ((x - 3) (x^{2} + 3 x + 3^{2}))$

Raise $3$ to the power of $2$ .

$y^{2} ((x - 3) (x^{2} + 3 x + 9))$

Remove unnecessary parentheses.

$y^{2} (x - 3) (x^{2} + 3 x + 9)$

Factor x^3y^2-27y^2

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