Factor p^3-343q^3

$p^{3} - 343 q^{3}$

Step 1

Rewrite $343 q^{3}$ as ${(7 q)}^{3}$ .

$p^{3} - {(7 q)}^{3}$

Step 2

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 $a = p$ and $b = 7 q$ .

$(p - (7 q)) (p^{2} + p (7 q) + {(7 q)}^{2})$

Step 3

Simplify.

Multiply $7$ by $- 1$ .

$(p - 7 q) (p^{2} + p (7 q) + {(7 q)}^{2})$

Rewrite using the commutative property of multiplication.

$(p - 7 q) (p^{2} + 7 p q + {(7 q)}^{2})$

Apply the product rule to $7 q$ .

$(p - 7 q) (p^{2} + 7 p q + 7^{2} q^{2})$

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

$(p - 7 q) (p^{2} + 7 p q + 49 q^{2})$

Factor p^3-343q^3

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