Basic Math Examples

$(- 2 \sqrt{2 m + 2}) (- 2 \sqrt{2 m + 2})$

Step 1

Factor $2$ out of $2 m + 2$ .

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Step 1.1

Factor $2$ out of $2 m$ .

$- 2 \sqrt{2 (m) + 2} (- 2 \sqrt{2 m + 2})$

Step 1.2

Factor $2$ out of $2$ .

$- 2 \sqrt{2 (m) + 2 (1)} (- 2 \sqrt{2 m + 2})$

Step 1.3

Factor $2$ out of $2 (m) + 2 (1)$ .

$- 2 \sqrt{2 (m + 1)} (- 2 \sqrt{2 m + 2})$

Step 2

Factor $2$ out of $2 m + 2$ .

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Step 2.1

Factor $2$ out of $2 m$ .

$- 2 \sqrt{2 (m + 1)} (- 2 \sqrt{2 (m) + 2})$

Step 2.2

Factor $2$ out of $2$ .

$- 2 \sqrt{2 (m + 1)} (- 2 \sqrt{2 (m) + 2 (1)})$

Step 2.3

Factor $2$ out of $2 (m) + 2 (1)$ .

$- 2 \sqrt{2 (m + 1)} (- 2 \sqrt{2 (m + 1)})$

Step 3

Multiply $- 2 \sqrt{2 (m + 1)} (- 2 \sqrt{2 (m + 1)})$ .

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Step 3.1

Multiply $- 2$ by $- 2$ .

$4 \sqrt{2 (m + 1)} \sqrt{2 (m + 1)}$

Step 3.2

Raise $\sqrt{2 (m + 1)}$ to the power of $1$ .

$4 ({\sqrt{2 (m + 1)}}^{1} \sqrt{2 (m + 1)})$

Step 3.3

Raise $\sqrt{2 (m + 1)}$ to the power of $1$ .

$4 ({\sqrt{2 (m + 1)}}^{1} {\sqrt{2 (m + 1)}}^{1})$

Step 3.4

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

$4 {\sqrt{2 (m + 1)}}^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$4 {\sqrt{2 (m + 1)}}^{2}$

Step 4

Rewrite ${\sqrt{2 (m + 1)}}^{2}$ as $2 (m + 1)$ .

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Step 4.1

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

$4 {({(2 (m + 1))}^{\frac{1}{2}})}^{2}$

Step 4.2

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

$4 {(2 (m + 1))}^{\frac{1}{2} \cdot 2}$

Step 4.3

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

$4 {(2 (m + 1))}^{\frac{2}{2}}$

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

$4 {(2 (m + 1))}^{\frac{2}{2}}$

Step 4.4.2

Rewrite the expression.

$4 {(2 (m + 1))}^{1}$

Step 4.5

Simplify.

$4 (2 (m + 1))$

Step 5

Apply the distributive property.

$4 (2 m + 2 \cdot 1)$

Step 6

Multiply $2$ by $1$ .

$4 (2 m + 2)$

Step 7

Apply the distributive property.

$4 (2 m) + 4 \cdot 2$

Step 8

Multiply.

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Step 8.1

Multiply $2$ by $4$ .

$8 m + 4 \cdot 2$

Step 8.2

Multiply $4$ by $2$ .

$8 m + 8$