Factor 64x^3-27

$64 x^{3} - 27$

Step 1

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

${(4 x)}^{3} - 27$

Step 2

Rewrite $27$ as $3^{3}$ .

${(4 x)}^{3} - 3^{3}$

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 $a = 4 x$ and $b = 3$ .

$(4 x - 3) ({(4 x)}^{2} + 4 x \cdot 3 + 3^{2})$

Step 4

Simplify.

Apply the product rule to $4 x$ .

$(4 x - 3) (4^{2} x^{2} + 4 x \cdot 3 + 3^{2})$

Raise $4$ to the power of $2$ .

$(4 x - 3) (16 x^{2} + 4 x \cdot 3 + 3^{2})$

Multiply $3$ by $4$ .

$(4 x - 3) (16 x^{2} + 12 x + 3^{2})$

Raise $3$ to the power of $2$ .

$(4 x - 3) (16 x^{2} + 12 x + 9)$

Factor 64x^3-27

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