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

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

Evaluate

$$19$$

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}.

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

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

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

Calculate 3 to the power of 2 and get 9.

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

The square of \sqrt{3} is 3.

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

Multiply 9 and 3 to get 27.

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

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

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

Calculate 2 to the power of 2 and get 4.

$$27-4\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$27-4\times 2$$

Multiply 4 and 2 to get 8.

$$27-8$$

Subtract 8 from 27 to get 19.

$$19$$

Factor

$$19$$