Algebra Examples

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

Step 1

Factor ${(x - y)}^{9}$ out of $x^{3} {(x - y)}^{9} - y^{3} {(x - y)}^{9}$ .

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Step 1.1

Factor ${(x - y)}^{9}$ out of $x^{3} {(x - y)}^{9}$ .

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

Step 1.2

Factor ${(x - y)}^{9}$ out of $- y^{3} {(x - y)}^{9}$ .

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

Step 1.3

Factor ${(x - y)}^{9}$ out of ${(x - y)}^{9} x^{3} + {(x - y)}^{9} (- y^{3})$ .

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

Step 2

Factor.

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Step 2.1

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 $b = y$ .

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

Step 2.2

Remove unnecessary parentheses.

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

Step 3

Multiply ${(x - y)}^{9}$ by $x - y$ by adding the exponents.

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Step 3.1

Multiply ${(x - y)}^{9}$ by $x - y$ .

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Step 3.1.1

Raise $x - y$ to the power of $1$ .

${(x - y)}^{9} {(x - y)}^{1} (x^{2} + x y + y^{2})$

Step 3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x - y)}^{9 + 1} (x^{2} + x y + y^{2})$

Step 3.2

Add $9$ and $1$ .

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