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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

Solved example of difference of cubes

$factor\left(x^3-y^3\right)$
2

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

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

Multiply $-1$ times $-1$

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

4

Multiply $-1$ times $-1$

$\left(x-\left(y^3\right)^{\frac{1}{3}}\right)\left(x^2+x\left(y^3\right)^{\frac{1}{3}}+\left(-\left(-1\right)y^3\right)^{\frac{2}{3}}\right)$
5

Multiply $-1$ times $-1$

$\left(x-\left(y^3\right)^{\frac{1}{3}}\right)\left(x^2+x\left(y^3\right)^{\frac{1}{3}}+\left(y^3\right)^{\frac{2}{3}}\right)$
6

Divide $1$ by $3$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\left(y^3\right)^{\frac{1}{3}}+\left(y^3\right)^{\frac{2}{3}}\right)$
7

Divide $1$ by $3$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{y^3}+\left(y^3\right)^{\frac{2}{3}}\right)$
8

Divide $2$ by $3$

$\left(x-\sqrt[3]{y^3}\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(y^3\right)^{2}}\right)$
9

Simplify $\sqrt[3]{y^3}$ 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 $\frac{1}{3}$

$-y^{3\frac{1}{3}}$
10

Multiply $3$ times $\frac{1}{3}$

$-y$
11

Multiply $3$ times $\frac{1}{3}$

$\left(x-y\right)\left(x^2+x\sqrt[3]{y^3}+\sqrt[3]{\left(y^3\right)^{2}}\right)$
12

Simplify $\sqrt[3]{y^3}$ 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 $\frac{1}{3}$

$-y^{3\frac{1}{3}}$
13

Multiply $3$ times $\frac{1}{3}$

$-y$
14

Simplify $\sqrt[3]{y^3}$ 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 $\frac{1}{3}$

$xy^{3\frac{1}{3}}$
15

Multiply $3$ times $\frac{1}{3}$

$xy$
16

Multiply $3$ times $\frac{1}{3}$

$\left(x-y\right)\left(x^2+xy+\sqrt[3]{\left(y^3\right)^{2}}\right)$
17

Simplify $\sqrt[3]{y^3}$ 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 $\frac{1}{3}$

$-y^{3\frac{1}{3}}$
18

Multiply $3$ times $\frac{1}{3}$

$-y$
19

Simplify $\sqrt[3]{y^3}$ 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 $\frac{1}{3}$

$xy^{3\frac{1}{3}}$
20

Multiply $3$ times $\frac{1}{3}$

$xy$
21

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 $\frac{2}{3}$

$y^{3\frac{2}{3}}$
22

Multiply $3$ times $\frac{2}{3}$

$y^{2}$
23

Multiply $3$ times $\frac{2}{3}$

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

##  Final Answer

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

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