Solve (2+1sqrt{7})(2-4sqrt{7})

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

Evaluate

$$-6\sqrt{7}-24\approx -39.874507866$$

Solution Steps

Apply the distributive property by multiplying each term of 2+1\sqrt{7} by each term of 2-4\sqrt{7}.

$$4-8\sqrt{7}+2\sqrt{7}-4\left(\sqrt{7}\right)^{2}$$

Combine -8\sqrt{7} and 2\sqrt{7} to get -6\sqrt{7}.

$$4-6\sqrt{7}-4\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$4-6\sqrt{7}-4\times 7$$

Multiply -4 and 7 to get -28.

$$4-6\sqrt{7}-28$$

Subtract 28 from 4 to get -24.

$$-24-6\sqrt{7}$$

Factor

$$6 {(-\sqrt{7} - 4)} = -39.874507866$$