Pre-Algebra Examples

$x^{12} + y^{12}$

Step 1

Rewrite $x^{12}$ as ${(x^{4})}^{3}$ .

${(x^{4})}^{3} + y^{12}$

Step 2

Rewrite $y^{12}$ as ${(y^{4})}^{3}$ .

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

Step 3

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 $a = x^{4}$ and $b = y^{4}$ .

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

Step 4

Simplify.

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Step 4.1

Multiply the exponents in ${(x^{4})}^{2}$ .

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Step 4.1.1

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

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

Step 4.1.2

Multiply $4$ by $2$ .

$(x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + {(y^{4})}^{2})$

Step 4.2

Multiply the exponents in ${(y^{4})}^{2}$ .

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Step 4.2.1

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

$(x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + y^{4 \cdot 2})$

Step 4.2.2

Multiply $4$ by $2$ .

$(x^{4} + y^{4}) (x^{8} - x^{4} y^{4} + y^{8})$