Pre-Algebra Examples

$x^{3} y^{3} - 343$

Step 1

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

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

Step 2

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

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

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

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

Step 4

Simplify.

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Step 4.1

Apply the product rule to $x y$ .

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

Step 4.2

Move $7$ to the left of $x y$ .

$(x y - 7) (x^{2} y^{2} + 7 (x y) + 7^{2})$

Step 4.3

Remove parentheses.

$(x y - 7) (x^{2} y^{2} + 7 x y + 7^{2})$

Step 4.4

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

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