Solve (3sqrt{9}-2sqrt{3})(3sqrt{9}+2sqrt{3})

$$( 3 \sqrt { 9 } - 2 \sqrt { 3 } ) ( 3 \sqrt { 9 } + 2 \sqrt { 3 } )$$

Evaluate

$$69$$

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}.

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

Calculate the square root of 9 and get 3.

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

Multiply 3 and 3 to get 9.

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

Calculate 9 to the power of 2 and get 81.

$$81-\left(2\sqrt{3}\right)^{2}$$

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

$$81-2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$81-4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$81-4\times 3$$

Multiply 4 and 3 to get 12.

$$81-12$$

Subtract 12 from 81 to get 69.

$$69$$

Factor

$$3\times 23$$