Pre-Algebra Examples

$343 y^{3} + 1000$

Step 1

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

${(7 y)}^{3} + 1000$

Step 2

Rewrite $1000$ as $10^{3}$ .

${(7 y)}^{3} + 10^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 7 y$ and $b = 10$ .

$(7 y + 10) ({(7 y)}^{2} - (7 y) \cdot 10 + 10^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $7 y$ .

$(7 y + 10) (7^{2} y^{2} - (7 y) \cdot 10 + 10^{2})$

Step 4.2

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

$(7 y + 10) (49 y^{2} - (7 y) \cdot 10 + 10^{2})$

Step 4.3

Multiply $7$ by $- 1$ .

$(7 y + 10) (49 y^{2} - 7 y \cdot 10 + 10^{2})$

Step 4.4

Multiply $10$ by $- 7$ .

$(7 y + 10) (49 y^{2} - 70 y + 10^{2})$

Step 4.5

Raise $10$ to the power of $2$ .

$(7 y + 10) (49 y^{2} - 70 y + 100)$