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

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

Evaluate

$$2$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(3\sqrt{2}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{2}\right)^{2}-4^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2-4^{2}$$

Multiply 9 and 2 to get 18.

$$18-4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$18-16$$

Subtract 16 from 18 to get 2.

$$2$$

Factor

$$2$$