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

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

Rewrite $4$ as $2^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

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

Simplify by cancelling exponent with radical.

Apply the product rule to $2 \sqrt{(2 + x) (2 - x)}$ .

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

Raise $2$ to the power of $2$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$4 ((2 + x) (2 - x))$

Expand $(2 + x) (2 - x)$ using the FOIL Method.

Apply the distributive property.

$4 (2 (2 - x) + x (2 - x))$

Apply the distributive property.

$4 (2 \cdot 2 + 2 (- x) + x (2 - x))$

Apply the distributive property.

$4 (2 \cdot 2 + 2 (- x) + x \cdot 2 + x (- x))$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 (4 + 2 (- x) + x \cdot 2 + x (- x))$

Multiply $- 1$ by $2$ .

$4 (4 - 2 x + x \cdot 2 + x (- x))$

Move $2$ to the left of $x$ .

$4 (4 - 2 x + 2 \cdot x + x (- x))$

Rewrite using the commutative property of multiplication.

$4 (4 - 2 x + 2 x - x \cdot x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 (4 - 2 x + 2 x - (x \cdot x))$

Multiply $x$ by $x$ .

$4 (4 - 2 x + 2 x - x^{2})$

Add $- 2 x$ and $2 x$ .

$4 (4 + 0 - x^{2})$

Add $4$ and $0$ .

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

Apply the distributive property.

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

Multiply.

Multiply $4$ by $4$ .

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

Multiply $- 1$ by $4$ .

$16 - 4 x^{2}$

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

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