Simplify (2 square root of 7+3)(2 square root of 7-3)

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

Expand $(2 \sqrt{7} + 3) (2 \sqrt{7} - 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$2 \sqrt{7} (2 \sqrt{7}) + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7} - 3)$

Apply the distributive property.

$2 \sqrt{7} (2 \sqrt{7}) + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Simplify and combine like terms.

Simplify each term.

Multiply $2 \sqrt{7} (2 \sqrt{7})$ .

Multiply $2$ by $2$ .

$4 \sqrt{7} \sqrt{7} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

$4 ({\sqrt{7}}^{1} \sqrt{7}) + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

$4 ({\sqrt{7}}^{1} {\sqrt{7}}^{1}) + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

$4 {\sqrt{7}}^{1 + 1} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Add $1$ and $1$ .

$4 {\sqrt{7}}^{2} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

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

$4 {(7^{\frac{1}{2}})}^{2} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

$4 \cdot 7^{\frac{1}{2} \cdot 2} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

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

$4 \cdot 7^{\frac{2}{2}} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \cdot 7^{\frac{2}{2}} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Rewrite the expression.

$4 \cdot 7^{1} + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Evaluate the exponent.

$4 \cdot 7 + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Multiply $4$ by $7$ .

$28 + 2 \sqrt{7} \cdot - 3 + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Multiply $- 3$ by $2$ .

$28 - 6 \sqrt{7} + 3 (2 \sqrt{7}) + 3 \cdot - 3$

Multiply $2$ by $3$ .

$28 - 6 \sqrt{7} + 6 \sqrt{7} + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$28 - 6 \sqrt{7} + 6 \sqrt{7} - 9$

Subtract $9$ from $28$ .

$19 - 6 \sqrt{7} + 6 \sqrt{7}$

Add $- 6 \sqrt{7}$ and $6 \sqrt{7}$ .

$19 + 0$

Add $19$ and $0$ .

$19$

Simplify (2 square root of 7+3)(2 square root of 7-3)

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