Solve left(2sqrt{2}+4right)left(sqrt{2}-4right)

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

Evaluate

$$-4\sqrt{2}-12\approx -17.656854249$$

Solution Steps

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

$$2\left(\sqrt{2}\right)^{2}-8\sqrt{2}+4\sqrt{2}-16$$

The square of \sqrt{2} is 2.

$$2\times 2-8\sqrt{2}+4\sqrt{2}-16$$

Multiply 2 and 2 to get 4.

$$4-8\sqrt{2}+4\sqrt{2}-16$$

Combine -8\sqrt{2} and 4\sqrt{2} to get -4\sqrt{2}.

$$4-4\sqrt{2}-16$$

Subtract 16 from 4 to get -12.

$$-12-4\sqrt{2}$$

Factor

$$4 {(-\sqrt{2} - 3)} = -17.656854249$$