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

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

Evaluate

$$2$$

Solution Steps

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

$$12\sqrt{2}+9\left(\sqrt{2}\right)^{2}-16-12\sqrt{2}$$

The square of \sqrt{2} is 2.

$$12\sqrt{2}+9\times 2-16-12\sqrt{2}$$

Multiply 9 and 2 to get 18.

$$12\sqrt{2}+18-16-12\sqrt{2}$$

Subtract 16 from 18 to get 2.

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

Combine 12\sqrt{2} and -12\sqrt{2} to get 0.

$$2$$

Factor

$$2$$