Simplify ( square root of 7x+3)( square root of 7x-3)

$(\sqrt{7 x} + 3) (\sqrt{7 x} - 3)$

Expand $(\sqrt{7 x} + 3) (\sqrt{7 x} - 3)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{7 x} (\sqrt{7 x} - 3) + 3 (\sqrt{7 x} - 3)$

Apply the distributive property.

$\sqrt{7 x} \sqrt{7 x} + \sqrt{7 x} \cdot - 3 + 3 (\sqrt{7 x} - 3)$

Apply the distributive property.

$\sqrt{7 x} \sqrt{7 x} + \sqrt{7 x} \cdot - 3 + 3 \sqrt{7 x} + 3 \cdot - 3$

Simplify terms.

Combine the opposite terms in $\sqrt{7 x} \sqrt{7 x} + \sqrt{7 x} \cdot - 3 + 3 \sqrt{7 x} + 3 \cdot - 3$ .

Reorder the factors in the terms $\sqrt{7 x} \cdot - 3$ and $3 \sqrt{7 x}$ .

$\sqrt{7 x} \sqrt{7 x} - 3 \sqrt{7 x} + 3 \sqrt{7 x} + 3 \cdot - 3$

Add $- 3 \sqrt{7 x}$ and $3 \sqrt{7 x}$ .

$\sqrt{7 x} \sqrt{7 x} + 0 + 3 \cdot - 3$

Add $\sqrt{7 x} \sqrt{7 x}$ and $0$ .

$\sqrt{7 x} \sqrt{7 x} + 3 \cdot - 3$

Simplify each term.

Multiply $\sqrt{7 x} \sqrt{7 x}$ .

Raise $\sqrt{7 x}$ to the power of $1$ .

${\sqrt{7 x}}^{1} \sqrt{7 x} + 3 \cdot - 3$

Raise $\sqrt{7 x}$ to the power of $1$ .

${\sqrt{7 x}}^{1} {\sqrt{7 x}}^{1} + 3 \cdot - 3$

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

${\sqrt{7 x}}^{1 + 1} + 3 \cdot - 3$

Add $1$ and $1$ .

${\sqrt{7 x}}^{2} + 3 \cdot - 3$

Rewrite ${\sqrt{7 x}}^{2}$ as $7 x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x}$ as ${(7 x)}^{\frac{1}{2}}$ .

${({(7 x)}^{\frac{1}{2}})}^{2} + 3 \cdot - 3$

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

${(7 x)}^{\frac{1}{2} \cdot 2} + 3 \cdot - 3$

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

${(7 x)}^{\frac{2}{2}} + 3 \cdot - 3$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 x)}^{\frac{2}{2}} + 3 \cdot - 3$

Rewrite the expression.

${(7 x)}^{1} + 3 \cdot - 3$

Simplify.

$7 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$7 x - 9$