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

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

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}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

The square of \sqrt{3} is 3.

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

Multiply 9 and 3 to get 27.

$$27-\left(3\sqrt{2}\right)^{2}$$

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

$$27-3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$27-9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$27-9\times 2$$

Multiply 9 and 2 to get 18.

$$27-18$$

Subtract 18 from 27 to get 9.

$$9$$

Factor

$$3^{2}$$