Algebra Examples

$8 x^{6} - y^{3}$

Step 1

Rewrite $8 x^{6}$ as ${(2 x^{2})}^{3}$ .

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

Step 2

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

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

Step 3

Simplify.

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Step 3.1

Apply the product rule to $2 x^{2}$ .

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

Step 3.2

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

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

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Multiply $2$ by $2$ .

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