Solve (3sqrt{2}-4)(sqrt{2}+4)

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

Evaluate

$$8\sqrt{2}-10\approx 1.313708499$$

Solution Steps

Apply the distributive property by multiplying each term of 3\sqrt{2}-4 by each term of \sqrt{2}+4.

$$3\left(\sqrt{2}\right)^{2}+12\sqrt{2}-4\sqrt{2}-16$$

The square of \sqrt{2} is 2.

$$3\times 2+12\sqrt{2}-4\sqrt{2}-16$$

Multiply 3 and 2 to get 6.

$$6+12\sqrt{2}-4\sqrt{2}-16$$

Combine 12\sqrt{2} and -4\sqrt{2} to get 8\sqrt{2}.

$$6+8\sqrt{2}-16$$

Subtract 16 from 6 to get -10.

$$-10+8\sqrt{2}$$