Algebra Examples

$8 y^{3} + 27$

Step 1

Rewrite $8 y^{3}$ as ${(2 y)}^{3}$ .

${(2 y)}^{3} + 27$

Step 2

Rewrite $27$ as $3^{3}$ .

${(2 y)}^{3} + 3^{3}$

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 $a = 2 y$ and $b = 3$ .

$(2 y + 3) ({(2 y)}^{2} - (2 y) \cdot 3 + 3^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $2 y$ .

$(2 y + 3) (2^{2} y^{2} - (2 y) \cdot 3 + 3^{2})$

Step 4.2

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

$(2 y + 3) (4 y^{2} - (2 y) \cdot 3 + 3^{2})$

Step 4.3

Multiply $2$ by $- 1$ .

$(2 y + 3) (4 y^{2} - 2 y \cdot 3 + 3^{2})$

Step 4.4

Multiply $3$ by $- 2$ .

$(2 y + 3) (4 y^{2} - 6 y + 3^{2})$

Step 4.5

Raise $3$ to the power of $2$ .

$(2 y + 3) (4 y^{2} - 6 y + 9)$