Simplify ( square root of a-b)( square root of a+b)

$(\sqrt{a} - b) (\sqrt{a} + b)$

Expand $(\sqrt{a} - b) (\sqrt{a} + b)$ using the FOIL Method.

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Apply the distributive property.

$\sqrt{a} (\sqrt{a} + b) - b (\sqrt{a} + b)$

Apply the distributive property.

$\sqrt{a} \sqrt{a} + \sqrt{a} b - b (\sqrt{a} + b)$

Apply the distributive property.

$\sqrt{a} \sqrt{a} + \sqrt{a} b - b \sqrt{a} - b \cdot b$

Simplify terms.

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Combine the opposite terms in $\sqrt{a} \sqrt{a} + \sqrt{a} b - b \sqrt{a} - b \cdot b$ .

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Reorder the factors in the terms $\sqrt{a} b$ and $- b \sqrt{a}$ .

$\sqrt{a} \sqrt{a} + b \sqrt{a} - b \sqrt{a} - b \cdot b$

Subtract $b \sqrt{a}$ from $b \sqrt{a}$ .

$\sqrt{a} \sqrt{a} + 0 - b \cdot b$

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

$\sqrt{a} \sqrt{a} - b \cdot b$

Simplify each term.

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Multiply $\sqrt{a} \sqrt{a}$ .

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

${\sqrt{a}}^{1} \sqrt{a} - b \cdot b$

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

${\sqrt{a}}^{1} {\sqrt{a}}^{1} - b \cdot b$

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

${\sqrt{a}}^{1 + 1} - b \cdot b$

Add $1$ and $1$ .

${\sqrt{a}}^{2} - b \cdot b$

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

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

${(a^{\frac{1}{2}})}^{2} - b \cdot b$

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

$a^{\frac{1}{2} \cdot 2} - b \cdot b$

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

$a^{\frac{2}{2}} - b \cdot b$

Cancel the common factor of $2$ .

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Cancel the common factor.

$a^{\frac{2}{2}} - b \cdot b$

Divide $1$ by $1$ .

$a^{1} - b \cdot b$

Simplify.

$a - b \cdot b$

Multiply $b$ by $b$ by adding the exponents.

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Move $b$ .

$a - (b \cdot b)$

Multiply $b$ by $b$ .

$a - b^{2}$

Simplify ( square root of a-b)( square root of a+b)

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