Basic Math Examples

$a^{12} + b^{12}$

Step 1

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

${(a^{4})}^{3} + b^{12}$

Step 2

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

${(a^{4})}^{3} + {(b^{4})}^{3}$

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

$(a^{4} + b^{4}) ({(a^{4})}^{2} - a^{4} b^{4} + {(b^{4})}^{2})$

Step 4

Simplify.

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Step 4.1

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

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Step 4.1.1

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

$(a^{4} + b^{4}) (a^{4 \cdot 2} - a^{4} b^{4} + {(b^{4})}^{2})$

Step 4.1.2

Multiply $4$ by $2$ .

$(a^{4} + b^{4}) (a^{8} - a^{4} b^{4} + {(b^{4})}^{2})$

Step 4.2

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

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Step 4.2.1

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

$(a^{4} + b^{4}) (a^{8} - a^{4} b^{4} + b^{4 \cdot 2})$

Step 4.2.2

Multiply $4$ by $2$ .

$(a^{4} + b^{4}) (a^{8} - a^{4} b^{4} + b^{8})$