Finite Math Examples

$108 w^{3} + 4 y^{6}$

Step 1

Factor $4$ out of $108 w^{3} + 4 y^{6}$ .

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Step 1.1

Factor $4$ out of $108 w^{3}$ .

$4 (27 w^{3}) + 4 y^{6}$

Step 1.2

Factor $4$ out of $4 y^{6}$ .

$4 (27 w^{3}) + 4 (y^{6})$

Step 1.3

Factor $4$ out of $4 (27 w^{3}) + 4 (y^{6})$ .

$4 (27 w^{3} + y^{6})$

Step 2

Rewrite $27 w^{3}$ as ${(3 w)}^{3}$ .

$4 ({(3 w)}^{3} + y^{6})$

Step 3

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

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

Step 4

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

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Apply the product rule to $3 w$ .

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

Step 5.1.2

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

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

Step 5.1.3

Multiply $3$ by $- 1$ .

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

Step 5.1.4

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

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Step 5.1.4.1

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

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

Step 5.1.4.2

Multiply $2$ by $2$ .

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

Step 5.2

Remove unnecessary parentheses.

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