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

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

Evaluate

$$9$$

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}.

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{2}\right)^{2}-3^{2}$$

The square of \sqrt{2} is 2.

$$9\times 2-3^{2}$$

Multiply 9 and 2 to get 18.

$$18-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$18-9$$

Subtract 9 from 18 to get 9.

$$9$$

Factor

$$3^{2}$$