Solve (2sqrt{3}+3sqrt{5})*(2sqrt{3}-3sqrt{5})

$$(2 \sqrt{ 3 } +3 \sqrt{ 5 } ) \times (2 \sqrt{ 3 } -3 \sqrt{ 5 } )$$

Evaluate

$$-33$$

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}.

$$\left(2\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

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

$$2^{2}\left(\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{3}\right)^{2}-\left(3\sqrt{5}\right)^{2}$$

The square of \sqrt{3} is 3.

$$4\times 3-\left(3\sqrt{5}\right)^{2}$$

Multiply 4 and 3 to get 12.

$$12-\left(3\sqrt{5}\right)^{2}$$

Expand \left(3\sqrt{5}\right)^{2}.

$$12-3^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$12-9\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$12-9\times 5$$

Multiply 9 and 5 to get 45.

$$12-45$$

Subtract 45 from 12 to get -33.

$$-33$$

Factor

$$-33$$