Simplify (2 square root of x+2)( square root of x+3)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$2 \sqrt{x} \sqrt{x} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Step 2

Simplify and combine like terms.

Simplify each term.

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

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

$2 ({\sqrt{x}}^{1} \sqrt{x}) + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

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

$2 ({\sqrt{x}}^{1} {\sqrt{x}}^{1}) + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

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

$2 {\sqrt{x}}^{1 + 1} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Add $1$ and $1$ .

$2 {\sqrt{x}}^{2} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

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

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

$2 {(x^{\frac{1}{2}})}^{2} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

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

$2 x^{\frac{1}{2} \cdot 2} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

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

$2 x^{\frac{2}{2}} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x^{\frac{2}{2}} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Rewrite the expression.

$2 x^{1} + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Simplify.

$2 x + 2 \sqrt{x} \cdot 3 + 2 \sqrt{x} + 2 \cdot 3$

Multiply $3$ by $2$ .

$2 x + 6 \sqrt{x} + 2 \sqrt{x} + 2 \cdot 3$

Multiply $2$ by $3$ .

$2 x + 6 \sqrt{x} + 2 \sqrt{x} + 6$

Add $6 \sqrt{x}$ and $2 \sqrt{x}$ .

$2 x + 8 \sqrt{x} + 6$