Factor 8x^3-343

$8 x^{3} - 343$

Step 1

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

${(2 x)}^{3} - 343$

Step 2

Rewrite $343$ as $7^{3}$ .

${(2 x)}^{3} - 7^{3}$

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 $a = 2 x$ and $b = 7$ .

$(2 x - 7) ({(2 x)}^{2} + 2 x \cdot 7 + 7^{2})$

Step 4

Simplify.

Apply the product rule to $2 x$ .

$(2 x - 7) (2^{2} x^{2} + 2 x \cdot 7 + 7^{2})$

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

$(2 x - 7) (4 x^{2} + 2 x \cdot 7 + 7^{2})$

Multiply $7$ by $2$ .

$(2 x - 7) (4 x^{2} + 14 x + 7^{2})$

Raise $7$ to the power of $2$ .

$(2 x - 7) (4 x^{2} + 14 x + 49)$

Factor 8x^3-343

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