Precalculus Examples

$1000 - 8 x^{6}$

Step 1

Factor $8$ out of $1000 - 8 x^{6}$ .

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Step 1.1

Factor $8$ out of $1000$ .

$8 (125) - 8 x^{6}$

Step 1.2

Factor $8$ out of $- 8 x^{6}$ .

$8 (125) + 8 (- x^{6})$

Step 1.3

Factor $8$ out of $8 (125) + 8 (- x^{6})$ .

$8 (125 - x^{6})$

Step 2

Rewrite $125$ as $5^{3}$ .

$8 (5^{3} - x^{6})$

Step 3

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

$8 (5^{3} - {(x^{2})}^{3})$

Step 4

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = 5$ and $b = x^{2}$ .

$8 ((5 - x^{2}) (5^{2} + 5 x^{2} + {(x^{2})}^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Raise $5$ to the power of $2$ .

$8 ((5 - x^{2}) (25 + 5 x^{2} + {(x^{2})}^{2}))$

Step 5.1.2

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

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Step 5.1.2.1

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

$8 ((5 - x^{2}) (25 + 5 x^{2} + x^{2 \cdot 2}))$

Step 5.1.2.2

Multiply $2$ by $2$ .

$8 ((5 - x^{2}) (25 + 5 x^{2} + x^{4}))$

Step 5.2

Remove unnecessary parentheses.

$8 (5 - x^{2}) (25 + 5 x^{2} + x^{4})$