Factor x^3y^3-64

$x^{3} y^{3} - 64$

Step 1

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

${(x y)}^{3} - 64$

Step 2

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

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

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

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

Step 4

Simplify.

Apply the product rule to $x y$ .

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

Move $4$ to the left of $x y$ .

$(x y - 4) (x^{2} y^{2} + 4 (x y) + 4^{2})$

Remove parentheses.

$(x y - 4) (x^{2} y^{2} + 4 x y + 4^{2})$

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

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

Factor x^3y^3-64

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