Calculus Examples

$35 w^{6} + 2240$

Step 1

Factor $35$ out of $35 w^{6} + 2240$ .

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Step 1.1

Factor $35$ out of $35 w^{6}$ .

$35 (w^{6}) + 2240$

Step 1.2

Factor $35$ out of $2240$ .

$35 w^{6} + 35 \cdot 64$

Step 1.3

Factor $35$ out of $35 w^{6} + 35 \cdot 64$ .

$35 (w^{6} + 64)$

Step 2

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

$35 ({(w^{2})}^{3} + 64)$

Step 3

Rewrite $64$ as $4^{3}$ .

$35 ({(w^{2})}^{3} + 4^{3})$

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 $a = w^{2}$ and $b = 4$ .

$35 ((w^{2} + 4) ({(w^{2})}^{2} - w^{2} \cdot 4 + 4^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

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Step 5.1.1.1

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

$35 ((w^{2} + 4) (w^{2 \cdot 2} - w^{2} \cdot 4 + 4^{2}))$

Step 5.1.1.2

Multiply $2$ by $2$ .

$35 ((w^{2} + 4) (w^{4} - w^{2} \cdot 4 + 4^{2}))$

Step 5.1.2

Multiply $4$ by $- 1$ .

$35 ((w^{2} + 4) (w^{4} - 4 w^{2} + 4^{2}))$

Step 5.1.3

Raise $4$ to the power of $2$ .

$35 ((w^{2} + 4) (w^{4} - 4 w^{2} + 16))$

Step 5.2

Remove unnecessary parentheses.

$35 (w^{2} + 4) (w^{4} - 4 w^{2} + 16)$