Precalculus Examples

$(x^{2} + 2 x h + h^{2}) (x + h)$

Step 1

Expand $(x^{2} + 2 x h + h^{2}) (x + h)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} h + 2 x h x + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Multiply $x^{2}$ by $x$ .

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Step 2.1.1.1.1

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + x^{2} h + 2 x h x + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2.1.1.1.2

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

$x^{2 + 1} + x^{2} h + 2 x h x + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} h + 2 x h x + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1

Move $x$ .

$x^{3} + x^{2} h + 2 (x \cdot x) h + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2.1.2.2

Multiply $x$ by $x$ .

$x^{3} + x^{2} h + 2 x^{2} h + 2 x h \cdot h + h^{2} x + h^{2} h$

Step 2.1.3

Multiply $h$ by $h$ by adding the exponents.

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Step 2.1.3.1

Move $h$ .

$x^{3} + x^{2} h + 2 x^{2} h + 2 x (h \cdot h) + h^{2} x + h^{2} h$

Step 2.1.3.2

Multiply $h$ by $h$ .

$x^{3} + x^{2} h + 2 x^{2} h + 2 x h^{2} + h^{2} x + h^{2} h$

Step 2.1.4

Multiply $h^{2}$ by $h$ by adding the exponents.

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Step 2.1.4.1

Multiply $h^{2}$ by $h$ .

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Step 2.1.4.1.1

Raise $h$ to the power of $1$ .

$x^{3} + x^{2} h + 2 x^{2} h + 2 x h^{2} + h^{2} x + h^{2} h^{1}$

Step 2.1.4.1.2

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

$x^{3} + x^{2} h + 2 x^{2} h + 2 x h^{2} + h^{2} x + h^{2 + 1}$

Step 2.1.4.2

Add $2$ and $1$ .

$x^{3} + x^{2} h + 2 x^{2} h + 2 x h^{2} + h^{2} x + h^{3}$

Step 2.2

Add $x^{2} h$ and $2 x^{2} h$ .

$x^{3} + 3 x^{2} h + 2 x h^{2} + h^{2} x + h^{3}$

Step 3

Add $2 x h^{2}$ and $h^{2} x$ .

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Step 3.1

Move $x$ .

$x^{3} + 3 x^{2} h + 2 h^{2} x + h^{2} x + h^{3}$

Step 3.2

Add $2 h^{2} x$ and $h^{2} x$ .

$x^{3} + 3 x^{2} h + 3 h^{2} x + h^{3}$

Step 4

Move $x^{2}$ .

$x^{3} + 3 h x^{2} + 3 h^{2} x + h^{3}$

Step 5

Move $x^{3}$ .

$3 h x^{2} + 3 h^{2} x + h^{3} + x^{3}$

Step 6

Move $3 h x^{2}$ .

$3 h^{2} x + h^{3} + 3 h x^{2} + x^{3}$

Step 7

Reorder $3 h^{2} x$ and $h^{3}$ .

$h^{3} + 3 h^{2} x + 3 h x^{2} + x^{3}$