Simplify (4- square root of 2x)^2

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

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- \sqrt{2 x}) - \sqrt{2 x} \cdot 4 - \sqrt{2 x} (- \sqrt{2 x})$

Multiply $- 1$ by $4$ .

$16 - 4 \sqrt{2 x} - \sqrt{2 x} \cdot 4 - \sqrt{2 x} (- \sqrt{2 x})$

Multiply $4$ by $- 1$ .

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} - \sqrt{2 x} (- \sqrt{2 x})$

Multiply $- \sqrt{2 x} (- \sqrt{2 x})$ .

Multiply $- 1$ by $- 1$ .

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + 1 \sqrt{2 x} \sqrt{2 x}$

Multiply $\sqrt{2 x}$ by $1$ .

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

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {\sqrt{2 x}}^{1} \sqrt{2 x}$

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {\sqrt{2 x}}^{1} {\sqrt{2 x}}^{1}$

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {\sqrt{2 x}}^{1 + 1}$

Add $1$ and $1$ .

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

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

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {({(2 x)}^{\frac{1}{2}})}^{2}$

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {(2 x)}^{\frac{1}{2} \cdot 2}$

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

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {(2 x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {(2 x)}^{\frac{2}{2}}$

Rewrite the expression.

$16 - 4 \sqrt{2 x} - 4 \sqrt{2 x} + {(2 x)}^{1}$

Simplify.

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

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

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

Move $- 8 \sqrt{2 x}$ .

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

Reorder $16$ and $2 x$ .

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

Simplify (4- square root of 2x)^2

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