Simplify the Radical Expression (3-2 square root of k)^2

${(3 - 2 \sqrt{k})}^{2}$

Rewrite ${(3 - 2 \sqrt{k})}^{2}$ as $(3 - 2 \sqrt{k}) (3 - 2 \sqrt{k})$ .

$(3 - 2 \sqrt{k}) (3 - 2 \sqrt{k})$

Expand $(3 - 2 \sqrt{k}) (3 - 2 \sqrt{k})$ using the FOIL Method.

Apply the distributive property.

$3 (3 - 2 \sqrt{k}) - 2 \sqrt{k} (3 - 2 \sqrt{k})$

Apply the distributive property.

$3 \cdot 3 + 3 (- 2 \sqrt{k}) - 2 \sqrt{k} (3 - 2 \sqrt{k})$

Apply the distributive property.

$3 \cdot 3 + 3 (- 2 \sqrt{k}) - 2 \sqrt{k} \cdot 3 - 2 \sqrt{k} (- 2 \sqrt{k})$

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- 2 \sqrt{k}) - 2 \sqrt{k} \cdot 3 - 2 \sqrt{k} (- 2 \sqrt{k})$

Multiply $- 2$ by $3$ .

$9 - 6 \sqrt{k} - 2 \sqrt{k} \cdot 3 - 2 \sqrt{k} (- 2 \sqrt{k})$

Multiply $3$ by $- 2$ .

$9 - 6 \sqrt{k} - 6 \sqrt{k} - 2 \sqrt{k} (- 2 \sqrt{k})$

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

Multiply $- 2$ by $- 2$ .

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 \sqrt{k} \sqrt{k}$

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 ({\sqrt{k}}^{1} \sqrt{k})$

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 ({\sqrt{k}}^{1} {\sqrt{k}}^{1})$

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 {\sqrt{k}}^{1 + 1}$

Add $1$ and $1$ .

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 {\sqrt{k}}^{2}$

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

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 {(k^{\frac{1}{2}})}^{2}$

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 k^{\frac{1}{2} \cdot 2}$

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

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 k^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 k^{\frac{2}{2}}$

Rewrite the expression.

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 k^{1}$

Simplify.

$9 - 6 \sqrt{k} - 6 \sqrt{k} + 4 k$

Subtract $6 \sqrt{k}$ from $- 6 \sqrt{k}$ .

$9 - 12 \sqrt{k} + 4 k$