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

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

Evaluate

$$2$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

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

Multiply 4 and 5 to get 20.

$$20-\left(3\sqrt{2}\right)^{2}$$

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

$$20-3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$20-9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$20-9\times 2$$

Multiply 9 and 2 to get 18.

$$20-18$$

Subtract 18 from 20 to get 2.

$$2$$

Factor

$$2$$