Finite Math Examples

${(5 + \sqrt{x + 3})}^{2}$

Step 1

Rewrite ${(5 + \sqrt{x + 3})}^{2}$ as $(5 + \sqrt{x + 3}) (5 + \sqrt{x + 3})$ .

$(5 + \sqrt{x + 3}) (5 + \sqrt{x + 3})$

Step 2

Expand $(5 + \sqrt{x + 3}) (5 + \sqrt{x + 3})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 (5 + \sqrt{x + 3}) + \sqrt{x + 3} (5 + \sqrt{x + 3})$

Step 2.2

Apply the distributive property.

$5 \cdot 5 + 5 \sqrt{x + 3} + \sqrt{x + 3} (5 + \sqrt{x + 3})$

Step 2.3

Apply the distributive property.

$5 \cdot 5 + 5 \sqrt{x + 3} + \sqrt{x + 3} \cdot 5 + \sqrt{x + 3} \sqrt{x + 3}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $5$ by $5$ .

$25 + 5 \sqrt{x + 3} + \sqrt{x + 3} \cdot 5 + \sqrt{x + 3} \sqrt{x + 3}$

Step 3.1.2

Move $5$ to the left of $\sqrt{x + 3}$ .

$25 + 5 \sqrt{x + 3} + 5 \cdot \sqrt{x + 3} + \sqrt{x + 3} \sqrt{x + 3}$

Step 3.1.3

Multiply $\sqrt{x + 3} \sqrt{x + 3}$ .

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Step 3.1.3.1

Raise $\sqrt{x + 3}$ to the power of $1$ .

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {\sqrt{x + 3}}^{1} \sqrt{x + 3}$

Step 3.1.3.2

Raise $\sqrt{x + 3}$ to the power of $1$ .

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {\sqrt{x + 3}}^{1} {\sqrt{x + 3}}^{1}$

Step 3.1.3.3

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

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {\sqrt{x + 3}}^{1 + 1}$

Step 3.1.3.4

Add $1$ and $1$ .

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {\sqrt{x + 3}}^{2}$

Step 3.1.4

Rewrite ${\sqrt{x + 3}}^{2}$ as $x + 3$ .

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Step 3.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 3}$ as ${(x + 3)}^{\frac{1}{2}}$ .

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {({(x + 3)}^{\frac{1}{2}})}^{2}$

Step 3.1.4.2

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

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {(x + 3)}^{\frac{1}{2} \cdot 2}$

Step 3.1.4.3

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

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {(x + 3)}^{\frac{2}{2}}$

Step 3.1.4.4

Cancel the common factor of $2$ .

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Step 3.1.4.4.1

Cancel the common factor.

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {(x + 3)}^{\frac{2}{2}}$

Step 3.1.4.4.2

Rewrite the expression.

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + {(x + 3)}^{1}$

Step 3.1.4.5

Simplify.

$25 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + x + 3$

Step 3.2

Add $25$ and $3$ .

$28 + 5 \sqrt{x + 3} + 5 \sqrt{x + 3} + x$

Step 3.3

Add $5 \sqrt{x + 3}$ and $5 \sqrt{x + 3}$ .

$28 + 10 \sqrt{x + 3} + x$

Step 4

Move $10 \sqrt{x + 3}$ .

$28 + x + 10 \sqrt{x + 3}$

Step 5

Reorder $28$ and $x$ .

$x + 28 + 10 \sqrt{x + 3}$