Pre-Algebra Examples

$8 + 27 y^{6}$

Step 1

Rewrite $8$ as $2^{3}$ .

$2^{3} + 27 y^{6}$

Step 2

Rewrite $27 y^{6}$ as ${(3 y^{2})}^{3}$ .

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

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 $a = 2$ and $b = 3 y^{2}$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $- 2$ .

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

Step 4.3

Apply the product rule to $3 y^{2}$ .

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

Step 4.4

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

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

Step 4.5

Multiply the exponents in ${(y^{2})}^{2}$ .

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Step 4.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.5.2

Multiply $2$ by $2$ .

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