Simplify (2 square root of 9-x)^2

${(2 \sqrt{9 - x})}^{2}$

Simplify the expression.

Apply the product rule to $2 \sqrt{9 - x}$ .

$2^{2} {\sqrt{9 - x}}^{2}$

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

$4 {\sqrt{9 - x}}^{2}$

Rewrite ${\sqrt{9 - x}}^{2}$ as $9 - x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 - x}$ as ${(9 - x)}^{\frac{1}{2}}$ .

$4 {({(9 - x)}^{\frac{1}{2}})}^{2}$

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

$4 {(9 - x)}^{\frac{1}{2} \cdot 2}$

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

$4 {(9 - x)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(9 - x)}^{\frac{2}{2}}$

Rewrite the expression.

$4 {(9 - x)}^{1}$

Simplify.

$4 (9 - x)$

Apply the distributive property.

$4 \cdot 9 + 4 (- x)$

Multiply.

Multiply $4$ by $9$ .

$36 + 4 (- x)$

Multiply $- 1$ by $4$ .

$36 - 4 x$