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

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

Evaluate

$$-30$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

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

Multiply 4 and 5 to get 20.

$$20-\left(5\sqrt{2}\right)^{2}$$

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

$$20-5^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$20-25\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$20-25\times 2$$

Multiply 25 and 2 to get 50.

$$20-50$$

Subtract 50 from 20 to get -30.

$$-30$$

Factor

$$-30$$