Factor 10x^8y^2+80x^2y^5

$10 x^{8} y^{2} + 80 x^{2} y^{5}$

Step 1

Factor $10 x^{2} y^{2}$ out of $10 x^{8} y^{2} + 80 x^{2} y^{5}$ .

Factor $10 x^{2} y^{2}$ out of $10 x^{8} y^{2}$ .

$10 x^{2} y^{2} (x^{6}) + 80 x^{2} y^{5}$

Factor $10 x^{2} y^{2}$ out of $80 x^{2} y^{5}$ .

$10 x^{2} y^{2} (x^{6}) + 10 x^{2} y^{2} (8 y^{3})$

Factor $10 x^{2} y^{2}$ out of $10 x^{2} y^{2} (x^{6}) + 10 x^{2} y^{2} (8 y^{3})$ .

$10 x^{2} y^{2} (x^{6} + 8 y^{3})$

Step 2

Rewrite $x^{6}$ as ${(x^{2})}^{3}$ .

$10 x^{2} y^{2} ({(x^{2})}^{3} + 8 y^{3})$

Step 3

Rewrite $8 y^{3}$ as ${(2 y)}^{3}$ .

$10 x^{2} y^{2} ({(x^{2})}^{3} + {(2 y)}^{3})$

Step 4

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

$10 x^{2} y^{2} ((x^{2} + 2 y) ({(x^{2})}^{2} - x^{2} (2 y) + {(2 y)}^{2}))$

Step 5

Factor.

Simplify.

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{2 \cdot 2} - x^{2} (2 y) + {(2 y)}^{2}))$

Multiply $2$ by $2$ .

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{4} - x^{2} (2 y) + {(2 y)}^{2}))$

Rewrite using the commutative property of multiplication.

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{4} - 1 \cdot 2 x^{2} y + {(2 y)}^{2}))$

Multiply $- 1$ by $2$ .

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{4} - 2 x^{2} y + {(2 y)}^{2}))$

Apply the product rule to $2 y$ .

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{4} - 2 x^{2} y + 2^{2} y^{2}))$

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

$10 x^{2} y^{2} ((x^{2} + 2 y) (x^{4} - 2 x^{2} y + 4 y^{2}))$

Remove unnecessary parentheses.

$10 x^{2} y^{2} (x^{2} + 2 y) (x^{4} - 2 x^{2} y + 4 y^{2})$

Factor 10x^8y^2+80x^2y^5

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