Solve 3*(2+sqrt{3})(2-sqrt{3})

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

Evaluate

$$3$$

Solution Steps

Use the distributive property to multiply 3 by 2+\sqrt{3}.

$$\left(6+3\sqrt{3}\right)\left(2-\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 6+3\sqrt{3} by each term of 2-\sqrt{3}.

$$12-6\sqrt{3}+6\sqrt{3}-3\left(\sqrt{3}\right)^{2}$$

Combine -6\sqrt{3} and 6\sqrt{3} to get 0.

$$12-3\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$12-3\times 3$$

Multiply -3 and 3 to get -9.

$$12-9$$

Subtract 9 from 12 to get 3.

$$3$$

Factor

$$3$$