Algebra Examples

$x^{9} - y^{9}$

Step 1

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

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

Step 2

Rewrite $y^{9}$ as ${(y^{3})}^{3}$ .

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

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 $a = x^{3}$ and $b = y^{3}$ .

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

Step 4

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 $b = y$ .

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

Step 5

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 5.1

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

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

Step 5.2

Multiply $3$ by $2$ .

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

Step 6

Multiply the exponents in ${(y^{3})}^{2}$ .

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Step 6.1

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

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

Step 6.2

Multiply $3$ by $2$ .

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