Factor m^3n^3-64

$m^{3} n^{3} - 64$

Step 1

Rewrite $m^{3} n^{3}$ as ${(m n)}^{3}$ .

${(m n)}^{3} - 64$

Step 2

Rewrite $64$ as $4^{3}$ .

${(m n)}^{3} - 4^{3}$

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 $a = m n$ and $b = 4$ .

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

Step 4

Simplify.

Apply the product rule to $m n$ .

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

Move $4$ to the left of $m n$ .

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

Remove parentheses.

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

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

$(m n - 4) (m^{2} n^{2} + 4 m n + 16)$

Factor m^3n^3-64

Related Questions

Support LCMGCF.com by disabling your adblocker.