Precalculus Examples

$(\sqrt{h^{2} + 1} + 1) (\sqrt{h^{2} + 1} - 1)$

Step 1

Expand $(\sqrt{h^{2} + 1} + 1) (\sqrt{h^{2} + 1} - 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\sqrt{h^{2} + 1} (\sqrt{h^{2} + 1} - 1) + 1 (\sqrt{h^{2} + 1} - 1)$

Step 1.2

Apply the distributive property.

$\sqrt{h^{2} + 1} \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 (\sqrt{h^{2} + 1} - 1)$

Step 1.3

Apply the distributive property.

$\sqrt{h^{2} + 1} \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $\sqrt{h^{2} + 1} \sqrt{h^{2} + 1}$ .

Tap for more steps...

Step 2.1.1.1

Raise $\sqrt{h^{2} + 1}$ to the power of $1$ .

${\sqrt{h^{2} + 1}}^{1} \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.1.2

Raise $\sqrt{h^{2} + 1}$ to the power of $1$ .

${\sqrt{h^{2} + 1}}^{1} {\sqrt{h^{2} + 1}}^{1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.1.3

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

${\sqrt{h^{2} + 1}}^{1 + 1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.1.4

Add $1$ and $1$ .

${\sqrt{h^{2} + 1}}^{2} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2

Rewrite ${\sqrt{h^{2} + 1}}^{2}$ as $h^{2} + 1$ .

Tap for more steps...

Step 2.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{h^{2} + 1}$ as ${(h^{2} + 1)}^{\frac{1}{2}}$ .

${({(h^{2} + 1)}^{\frac{1}{2}})}^{2} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2.2

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

${(h^{2} + 1)}^{\frac{1}{2} \cdot 2} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2.3

Combine $\frac{1}{2}$ and $2$ .

${(h^{2} + 1)}^{\frac{2}{2}} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.2.4.1

Cancel the common factor.

${(h^{2} + 1)}^{\frac{2}{2}} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2.4.2

Rewrite the expression.

${(h^{2} + 1)}^{1} + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.2.5

Simplify.

$h^{2} + 1 + \sqrt{h^{2} + 1} \cdot - 1 + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.3

Move $- 1$ to the left of $\sqrt{h^{2} + 1}$ .

$h^{2} + 1 - 1 \cdot \sqrt{h^{2} + 1} + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.4

Rewrite $- 1 \sqrt{h^{2} + 1}$ as $- \sqrt{h^{2} + 1}$ .

$h^{2} + 1 - \sqrt{h^{2} + 1} + 1 \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.5

Multiply $\sqrt{h^{2} + 1}$ by $1$ .

$h^{2} + 1 - \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1} + 1 \cdot - 1$

Step 2.1.6

Multiply $- 1$ by $1$ .

$h^{2} + 1 - \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1} - 1$

Step 2.2

Subtract $1$ from $1$ .

$h^{2} + 0 - \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1}$

Step 2.3

Add $h^{2}$ and $0$ .

$h^{2} - \sqrt{h^{2} + 1} + \sqrt{h^{2} + 1}$

Step 2.4

Add $- \sqrt{h^{2} + 1}$ and $\sqrt{h^{2} + 1}$ .

$h^{2} + 0$

Step 2.5

Add $h^{2}$ and $0$ .

$h^{2}$