Factor x^6+1000

$x^{6} + 1000$

Step 1

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

${(x^{2})}^{3} + 1000$

Step 2

Rewrite $1000$ as $10^{3}$ .

${(x^{2})}^{3} + 10^{3}$

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 $a = x^{2}$ and $b = 10$ .

$(x^{2} + 10) ({(x^{2})}^{2} - x^{2} \cdot 10 + 10^{2})$

Step 4

Simplify.

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

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

$(x^{2} + 10) (x^{2 \cdot 2} - x^{2} \cdot 10 + 10^{2})$

Multiply $2$ by $2$ .

$(x^{2} + 10) (x^{4} - x^{2} \cdot 10 + 10^{2})$

Multiply $10$ by $- 1$ .

$(x^{2} + 10) (x^{4} - 10 x^{2} + 10^{2})$

Raise $10$ to the power of $2$ .

$(x^{2} + 10) (x^{4} - 10 x^{2} + 100)$

Factor x^6+1000

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