Algebra Examples

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

Step 1

Expand $(x^{\frac{2}{3}} - x^{\frac{1}{3}}) (x^{\frac{2}{3}} + x^{\frac{1}{3}})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

$x^{\frac{2}{3}} x^{\frac{2}{3}} + x^{\frac{2}{3}} x^{\frac{1}{3}} - x^{\frac{1}{3}} x^{\frac{2}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x^{\frac{2}{3}} x^{\frac{2}{3}} + x^{\frac{2}{3}} x^{\frac{1}{3}} - x^{\frac{1}{3}} x^{\frac{2}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$ .

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Step 2.1.1

Reorder the factors in the terms $x^{\frac{2}{3}} x^{\frac{1}{3}}$ and $- x^{\frac{1}{3}} x^{\frac{2}{3}}$ .

$x^{\frac{2}{3}} x^{\frac{2}{3}} + x^{\frac{2}{3}} x^{\frac{1}{3}} - x^{\frac{2}{3}} x^{\frac{1}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.1.2

Subtract $x^{\frac{2}{3}} x^{\frac{1}{3}}$ from $x^{\frac{2}{3}} x^{\frac{1}{3}}$ .

$x^{\frac{2}{3}} x^{\frac{2}{3}} + 0 - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.1.3

Add $x^{\frac{2}{3}} x^{\frac{2}{3}}$ and $0$ .

$x^{\frac{2}{3}} x^{\frac{2}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x^{\frac{2}{3}}$ by $x^{\frac{2}{3}}$ by adding the exponents.

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Step 2.2.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{\frac{2}{3} + \frac{2}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.2.1.2

Combine the numerators over the common denominator.

$x^{\frac{2 + 2}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.2.1.3

Add $2$ and $2$ .

$x^{\frac{4}{3}} - x^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2.2.2

Multiply $x^{\frac{1}{3}}$ by $x^{\frac{1}{3}}$ by adding the exponents.

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Step 2.2.2.1

Move $x^{\frac{1}{3}}$ .

$x^{\frac{4}{3}} - (x^{\frac{1}{3}} x^{\frac{1}{3}})$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{\frac{4}{3}} - x^{\frac{1}{3} + \frac{1}{3}}$

Step 2.2.2.3

Combine the numerators over the common denominator.

$x^{\frac{4}{3}} - x^{\frac{1 + 1}{3}}$

Step 2.2.2.4

Add $1$ and $1$ .

$x^{\frac{4}{3}} - x^{\frac{2}{3}}$