Basic Math Examples

$(\sqrt{c} - u) (\sqrt{c} + u)$

Step 1

Expand $(\sqrt{c} - u) (\sqrt{c} + u)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{c} (\sqrt{c} + u) - u (\sqrt{c} + u)$

Step 1.2

Apply the distributive property.

$\sqrt{c} \sqrt{c} + \sqrt{c} u - u (\sqrt{c} + u)$

Step 1.3

Apply the distributive property.

$\sqrt{c} \sqrt{c} + \sqrt{c} u - u \sqrt{c} - u \cdot u$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\sqrt{c} \sqrt{c} + \sqrt{c} u - u \sqrt{c} - u \cdot u$ .

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Step 2.1.1

Reorder the factors in the terms $\sqrt{c} u$ and $- u \sqrt{c}$ .

$\sqrt{c} \sqrt{c} + u \sqrt{c} - u \sqrt{c} - u \cdot u$

Step 2.1.2

Subtract $u \sqrt{c}$ from $u \sqrt{c}$ .

$\sqrt{c} \sqrt{c} + 0 - u \cdot u$

Step 2.1.3

Add $\sqrt{c} \sqrt{c}$ and $0$ .

$\sqrt{c} \sqrt{c} - u \cdot u$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $\sqrt{c} \sqrt{c}$ .

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Step 2.2.1.1

Raise $\sqrt{c}$ to the power of $1$ .

${\sqrt{c}}^{1} \sqrt{c} - u \cdot u$

Step 2.2.1.2

Raise $\sqrt{c}$ to the power of $1$ .

${\sqrt{c}}^{1} {\sqrt{c}}^{1} - u \cdot u$

Step 2.2.1.3

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

${\sqrt{c}}^{1 + 1} - u \cdot u$

Step 2.2.1.4

Add $1$ and $1$ .

${\sqrt{c}}^{2} - u \cdot u$

Step 2.2.2

Rewrite ${\sqrt{c}}^{2}$ as $c$ .

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Step 2.2.2.1

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

${(c^{\frac{1}{2}})}^{2} - u \cdot u$

Step 2.2.2.2

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

$c^{\frac{1}{2} \cdot 2} - u \cdot u$

Step 2.2.2.3

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

$c^{\frac{2}{2}} - u \cdot u$

Step 2.2.2.4

Cancel the common factor of $2$ .

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Step 2.2.2.4.1

Cancel the common factor.

$c^{\frac{2}{2}} - u \cdot u$

Step 2.2.2.4.2

Rewrite the expression.

$c^{1} - u \cdot u$

Step 2.2.2.5

Simplify.

$c - u \cdot u$

Step 2.2.3

Multiply $u$ by $u$ by adding the exponents.

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Step 2.2.3.1

Move $u$ .

$c - (u \cdot u)$

Step 2.2.3.2

Multiply $u$ by $u$ .

$c - u^{2}$