Simplify (2-3 square root of x)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- 3 \sqrt{x}) - 3 \sqrt{x} \cdot 2 - 3 \sqrt{x} (- 3 \sqrt{x})$

Multiply $- 3$ by $2$ .

$4 - 6 \sqrt{x} - 3 \sqrt{x} \cdot 2 - 3 \sqrt{x} (- 3 \sqrt{x})$

Multiply $2$ by $- 3$ .

$4 - 6 \sqrt{x} - 6 \sqrt{x} - 3 \sqrt{x} (- 3 \sqrt{x})$

Multiply $- 3 \sqrt{x} (- 3 \sqrt{x})$ .

Multiply $- 3$ by $- 3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

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

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

Step 4

Move $- 12 \sqrt{x}$ .

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

Step 5

Reorder $4$ and $9 x$ .

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

Simplify (2-3 square root of x)^2

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