Solve (6sqrt{2}-4sqrt{3})(6sqrt{2}+4sqrt{3})

$$( 6 \sqrt { 2 } - 4 \sqrt { 3 } ) ( 6 \sqrt { 2 } + 4 \sqrt { 3 } )$$

Evaluate

$$24$$

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}.

$$\left(6\sqrt{2}\right)^{2}-\left(4\sqrt{3}\right)^{2}$$

Expand \left(6\sqrt{2}\right)^{2}.

$$6^{2}\left(\sqrt{2}\right)^{2}-\left(4\sqrt{3}\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$36\left(\sqrt{2}\right)^{2}-\left(4\sqrt{3}\right)^{2}$$

The square of \sqrt{2} is 2.

$$36\times 2-\left(4\sqrt{3}\right)^{2}$$

Multiply 36 and 2 to get 72.

$$72-\left(4\sqrt{3}\right)^{2}$$

Expand \left(4\sqrt{3}\right)^{2}.

$$72-4^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$72-16\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$72-16\times 3$$

Multiply 16 and 3 to get 48.

$$72-48$$

Subtract 48 from 72 to get 24.

$$24$$

Factor

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