Basic Math Examples

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

Step 1

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

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

Step 2

Expand $(2 \sqrt{m} + 2) (2 \sqrt{m} + 2)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $2 \sqrt{m} (2 \sqrt{m})$ .

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Step 3.1.1.1

Multiply $2$ by $2$ .

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

Step 3.1.1.2

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

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

Step 3.1.1.3

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

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

Step 3.1.1.4

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

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

Step 3.1.1.5

Add $1$ and $1$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

Step 3.1.2.4

Cancel the common factor of $2$ .

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Step 3.1.2.4.1

Cancel the common factor.

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

Step 3.1.2.4.2

Rewrite the expression.

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

Step 3.1.2.5

Simplify.

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

Multiply $2$ by $2$ .

$4 m + 4 \sqrt{m} + 4 \sqrt{m} + 2 \cdot 2$

Step 3.1.5

Multiply $2$ by $2$ .

$4 m + 4 \sqrt{m} + 4 \sqrt{m} + 4$

Step 3.2

Add $4 \sqrt{m}$ and $4 \sqrt{m}$ .

$4 m + 8 \sqrt{m} + 4$