Algebra Examples

$x^{6} y^{3} + y^{9}$

Step 1

Factor out the GCF of $y^{3}$ from $x^{6} y^{3} + y^{9}$ .

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Step 1.1

Factor out the GCF of $y^{3}$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $y^{3}$ from the expression $x^{6} y^{3}$ .

$y^{3} (x^{6}) + y^{9}$

Step 1.1.2

Factor out the GCF of $y^{3}$ from the expression $y^{9}$ .

$y^{3} (x^{6}) + y^{3} (y^{6})$

Step 1.2

Since all the terms share a common factor of $y^{3}$ , it can be factored out of each term.

$y^{3} (x^{6} + y^{6})$

Step 2

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

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

Step 3

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

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

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 $b = y^{2}$ .

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

Step 5

Simplify.

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Step 5.1

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

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Step 5.1.1

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

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

Step 5.1.2

Multiply $2$ by $2$ .

$y^{3} ((x^{2} + y^{2}) (x^{4} - x^{2} y^{2} + {(y^{2})}^{2}))$

Step 5.2

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

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Step 5.2.1

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

$y^{3} ((x^{2} + y^{2}) (x^{4} - x^{2} y^{2} + y^{2 \cdot 2}))$

Step 5.2.2

Multiply $2$ by $2$ .

$y^{3} ((x^{2} + y^{2}) (x^{4} - x^{2} y^{2} + y^{4}))$