Algebra Examples

$8 - m^{6}$

Step 1

Rewrite $8$ as $2^{3}$ .

$2^{3} - m^{6}$

Step 2

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

$2^{3} - {(m^{2})}^{3}$

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 $a = 2$ and $b = m^{2}$ .

$(2 - m^{2}) (2^{2} + 2 m^{2} + {(m^{2})}^{2})$

Step 4

Simplify.

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Step 4.1

Raise $2$ to the power of $2$ .

$(2 - m^{2}) (4 + 2 m^{2} + {(m^{2})}^{2})$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $2$ .

$(2 - m^{2}) (4 + 2 m^{2} + m^{4})$