Pre-Algebra Examples

$512 y^{3} - 343$

Step 1

Rewrite $512 y^{3}$ as ${(8 y)}^{3}$ .

${(8 y)}^{3} - 343$

Step 2

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

${(8 y)}^{3} - 7^{3}$

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 $a = 8 y$ and $b = 7$ .

$(8 y - 7) ({(8 y)}^{2} + 8 y \cdot 7 + 7^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $8 y$ .

$(8 y - 7) (8^{2} y^{2} + 8 y \cdot 7 + 7^{2})$

Step 4.2

Raise $8$ to the power of $2$ .

$(8 y - 7) (64 y^{2} + 8 y \cdot 7 + 7^{2})$

Step 4.3

Multiply $7$ by $8$ .

$(8 y - 7) (64 y^{2} + 56 y + 7^{2})$

Step 4.4

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

$(8 y - 7) (64 y^{2} + 56 y + 49)$