Factor x^5-125x^2y^3

$x^{5} - 125 x^{2} y^{3}$

Step 1

Factor $x^{2}$ out of $x^{5} - 125 x^{2} y^{3}$ .

Factor $x^{2}$ out of $x^{5}$ .

$x^{2} x^{3} - 125 x^{2} y^{3}$

Factor $x^{2}$ out of $- 125 x^{2} y^{3}$ .

$x^{2} x^{3} + x^{2} (- 125 y^{3})$

Factor $x^{2}$ out of $x^{2} x^{3} + x^{2} (- 125 y^{3})$ .

$x^{2} (x^{3} - 125 y^{3})$

Step 2

Rewrite $125 y^{3}$ as ${(5 y)}^{3}$ .

$x^{2} (x^{3} - {(5 y)}^{3})$

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 $b = 5 y$ .

$x^{2} ((x - (5 y)) (x^{2} + x (5 y) + {(5 y)}^{2}))$

Step 4

Factor.

Simplify.

Multiply $5$ by $- 1$ .

$x^{2} ((x - 5 y) (x^{2} + x (5 y) + {(5 y)}^{2}))$

Rewrite using the commutative property of multiplication.

$x^{2} ((x - 5 y) (x^{2} + 5 x y + {(5 y)}^{2}))$

Apply the product rule to $5 y$ .

$x^{2} ((x - 5 y) (x^{2} + 5 x y + 5^{2} y^{2}))$

Raise $5$ to the power of $2$ .

$x^{2} ((x - 5 y) (x^{2} + 5 x y + 25 y^{2}))$

Remove unnecessary parentheses.

$x^{2} (x - 5 y) (x^{2} + 5 x y + 25 y^{2})$

Factor x^5-125x^2y^3

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