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

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

Evaluate

$$11$$

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

$$4\times 5-3^{2}$$

Multiply 4 and 5 to get 20.

$$20-3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$20-9$$

Subtract 9 from 20 to get 11.

$$11$$

Factor

$$11$$