Pre-Algebra Examples

${(\sqrt{2 x} - 4)}^{2}$

Step 1

Rewrite ${(\sqrt{2 x} - 4)}^{2}$ as $(\sqrt{2 x} - 4) (\sqrt{2 x} - 4)$ .

$(\sqrt{2 x} - 4) (\sqrt{2 x} - 4)$

Step 2

Expand $(\sqrt{2 x} - 4) (\sqrt{2 x} - 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\sqrt{2 x} (\sqrt{2 x} - 4) - 4 (\sqrt{2 x} - 4)$

Step 2.2

Apply the distributive property.

$\sqrt{2 x} \sqrt{2 x} + \sqrt{2 x} \cdot - 4 - 4 (\sqrt{2 x} - 4)$

Step 2.3

Apply the distributive property.

$\sqrt{2 x} \sqrt{2 x} + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

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 $\sqrt{2 x} \sqrt{2 x}$ .

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Step 3.1.1.1

Raise $\sqrt{2 x}$ to the power of $1$ .

${\sqrt{2 x}}^{1} \sqrt{2 x} + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.1.2

Raise $\sqrt{2 x}$ to the power of $1$ .

${\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1} + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.1.3

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

${\sqrt{2 x}}^{1 + 1} + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.1.4

Add $1$ and $1$ .

${\sqrt{2 x}}^{2} + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.2.3

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

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

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.

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

Step 3.1.2.4.2

Rewrite the expression.

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

Step 3.1.2.5

Simplify.

$2 x + \sqrt{2 x} \cdot - 4 - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.3

Move $- 4$ to the left of $\sqrt{2 x}$ .

$2 x - 4 \cdot \sqrt{2 x} - 4 \sqrt{2 x} - 4 \cdot - 4$

Step 3.1.4

Multiply $- 4$ by $- 4$ .

$2 x - 4 \sqrt{2 x} - 4 \sqrt{2 x} + 16$

Step 3.2

Subtract $4 \sqrt{2 x}$ from $- 4 \sqrt{2 x}$ .

$2 x - 8 \sqrt{2 x} + 16$