Factor 8m^3-1 - MathMaster

$8 m^{3} - 1$

Rewrite $8 m^{3}$ as ${(2 m)}^{3}$ .

${(2 m)}^{3} - 1$

Rewrite $1$ as $1^{3}$ .

${(2 m)}^{3} - 1^{3}$

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 $a = 2 m$ and $b = 1$ .

$(2 m - 1) ({(2 m)}^{2} + 2 m \cdot 1 + 1^{2})$

Simplify.

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Apply the product rule to $2 m$ .

$(2 m - 1) (2^{2} m^{2} + 2 m \cdot 1 + 1^{2})$

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

$(2 m - 1) (4 m^{2} + 2 m \cdot 1 + 1^{2})$

Multiply $2$ by $1$ .

$(2 m - 1) (4 m^{2} + 2 m + 1^{2})$

One to any power is one.

$(2 m - 1) (4 m^{2} + 2 m + 1)$

Factor 8m^3-1

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