Pre-Algebra Examples

$(\sqrt{p} - s) (\sqrt{p} + s)$

Step 1

Expand $(\sqrt{p} - s) (\sqrt{p} + s)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{p} (\sqrt{p} + s) - s (\sqrt{p} + s)$

Step 1.2

Apply the distributive property.

$\sqrt{p} \sqrt{p} + \sqrt{p} s - s (\sqrt{p} + s)$

Step 1.3

Apply the distributive property.

$\sqrt{p} \sqrt{p} + \sqrt{p} s - s \sqrt{p} - s \cdot s$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\sqrt{p} \sqrt{p} + \sqrt{p} s - s \sqrt{p} - s \cdot s$ .

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Step 2.1.1

Reorder the factors in the terms $\sqrt{p} s$ and $- s \sqrt{p}$ .

$\sqrt{p} \sqrt{p} + s \sqrt{p} - s \sqrt{p} - s \cdot s$

Step 2.1.2

Subtract $s \sqrt{p}$ from $s \sqrt{p}$ .

$\sqrt{p} \sqrt{p} + 0 - s \cdot s$

Step 2.1.3

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

$\sqrt{p} \sqrt{p} - s \cdot s$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $\sqrt{p} \sqrt{p}$ .

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Step 2.2.1.1

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

${\sqrt{p}}^{1} \sqrt{p} - s \cdot s$

Step 2.2.1.2

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

${\sqrt{p}}^{1} {\sqrt{p}}^{1} - s \cdot s$

Step 2.2.1.3

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

${\sqrt{p}}^{1 + 1} - s \cdot s$

Step 2.2.1.4

Add $1$ and $1$ .

${\sqrt{p}}^{2} - s \cdot s$

Step 2.2.2

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

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Step 2.2.2.1

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

${(p^{\frac{1}{2}})}^{2} - s \cdot s$

Step 2.2.2.2

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

$p^{\frac{1}{2} \cdot 2} - s \cdot s$

Step 2.2.2.3

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

$p^{\frac{2}{2}} - s \cdot s$

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.

$p^{\frac{2}{2}} - s \cdot s$

Step 2.2.2.4.2

Rewrite the expression.

$p^{1} - s \cdot s$

Step 2.2.2.5

Simplify.

$p - s \cdot s$

Step 2.2.3

Multiply $s$ by $s$ by adding the exponents.

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Step 2.2.3.1

Move $s$ .

$p - (s \cdot s)$

Step 2.2.3.2

Multiply $s$ by $s$ .

$p - s^{2}$