Factor by Grouping 216x^3-64

$216 x^{3} - 64$

Step 1

Factor out the GCF of $8$ from $216 x^{3} - 64$ .

Factor out the GCF of $8$ from each term in the polynomial.

Factor out the GCF of $8$ from the expression $216 x^{3}$ .

$8 (27 x^{3}) - 64$

Factor out the GCF of $8$ from the expression $- 64$ .

$8 (27 x^{3}) + 8 (- 8)$

Since all the terms share a common factor of $8$ , it can be factored out of each term.

$8 (27 x^{3} - 8)$

Step 2

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$8 ({(3 x)}^{3} - 8)$

Step 3

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

$8 ({(3 x)}^{3} - 2^{3})$

Step 4

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 $a = 3 x$ and $b = 2$ .

$8 ((3 x - 2) ({(3 x)}^{2} + 3 x \cdot 2 + 2^{2}))$

Step 5

Simplify.

Apply the product rule to $3 x$ .

$8 ((3 x - 2) (3^{2} x^{2} + 3 x \cdot 2 + 2^{2}))$

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

$8 ((3 x - 2) (9 x^{2} + 3 x \cdot 2 + 2^{2}))$

Multiply $2$ by $3$ .

$8 ((3 x - 2) (9 x^{2} + 6 x + 2^{2}))$

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

$8 ((3 x - 2) (9 x^{2} + 6 x + 4))$

Factor by Grouping 216x^3-64

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