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# Difference of Cubes Calculator

## Get detailed solutions to your math problems with our Difference of Cubes step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of difference of cubes. This solution was automatically generated by our smart calculator:

$factor\left(x^3-y^3\right)$

Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$

$\left(x-\sqrt[3]{-\left(-1\right)y^3}\right)\left(x^2+x\sqrt[3]{-\left(-1\right)y^3}+\sqrt[3]{\left(-\left(-1\right)y^3\right)^{2}}\right)$

Multiply $-1$ times $-1$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{-\left(-1\right)y^3}+\sqrt[3]{\left(-\left(-1\right)y^3\right)^{2}}\right)$

Multiply $-1$ times $-1$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(-\left(-1\right)y^3\right)^{2}}\right)$

Multiply $-1$ times $-1$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(y^3\right)^{2}}\right)$
2

Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(y^3\right)^{2}}\right)$
3

Cancel exponents $3$ and $1$

$\left(x-y\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(y^3\right)^{2}}\right)$
4

Cancel exponents $3$ and $1$

$\left(x-y\right)\left(x^2+xy+\sqrt[3]{\left(y^3\right)^{2}}\right)$

Simplify $\sqrt[3]{\left(y^3\right)^{2}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3$ and $n$ equals $\frac{2}{3}$

$\left(x-y\right)\left(x^2+xy+y^{3\cdot \left(\frac{2}{3}\right)}\right)$

Multiply the fraction and term in $3\cdot \left(\frac{2}{3}\right)$

$\left(x-y\right)\left(x^2+xy+y^{\frac{3\cdot 2}{3}}\right)$

Multiply $3$ times $2$

$\left(x-y\right)\left(x^2+xy+y^{\frac{6}{3}}\right)$

Divide $6$ by $3$

$\left(x-y\right)\left(x^2+xy+y^{2}\right)$
5

Simplify $\sqrt[3]{\left(y^3\right)^{2}}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $3$ and $n$ equals $\frac{2}{3}$

$\left(x-y\right)\left(x^2+xy+y^{2}\right)$

##  Final answer to the problem

$\left(x-y\right)\left(x^2+xy+y^{2}\right)$

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