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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- \sqrt{7}) + \sqrt{7} \cdot 3 + \sqrt{7} (- \sqrt{7})$

Multiply $- 1$ by $3$ .

$9 - 3 \sqrt{7} + \sqrt{7} \cdot 3 + \sqrt{7} (- \sqrt{7})$

Move $3$ to the left of $\sqrt{7}$ .

$9 - 3 \sqrt{7} + 3 \cdot \sqrt{7} + \sqrt{7} (- \sqrt{7})$

Multiply $\sqrt{7} (- \sqrt{7})$ .

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - ({\sqrt{7}}^{1} \sqrt{7})$

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - {\sqrt{7}}^{1 + 1}$

Add $1$ and $1$ .

$9 - 3 \sqrt{7} + 3 \sqrt{7} - {\sqrt{7}}^{2}$

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

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - {(7^{\frac{1}{2}})}^{2}$

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 7^{\frac{1}{2} \cdot 2}$

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

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 7^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 7^{\frac{2}{2}}$

Rewrite the expression.

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 7^{1}$

Evaluate the exponent.

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 1 \cdot 7$

Multiply $- 1$ by $7$ .

$9 - 3 \sqrt{7} + 3 \sqrt{7} - 7$

Subtract $7$ from $9$ .

$2 - 3 \sqrt{7} + 3 \sqrt{7}$

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

$2 + 0$

Add $2$ and $0$ .

$2$

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

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