Solve (4sqrt{5}+2sqrt{11})(4sqrt{5}-2sqrt{11})

$$( 4 \sqrt { 5 } + 2 \sqrt { 11 } ) ( 4 \sqrt { 5 } - 2 \sqrt { 11 } )$$

Evaluate

$$36$$

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}.

$$\left(4\sqrt{5}\right)^{2}-\left(2\sqrt{11}\right)^{2}$$

Expand \left(4\sqrt{5}\right)^{2}.

$$4^{2}\left(\sqrt{5}\right)^{2}-\left(2\sqrt{11}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{5}\right)^{2}-\left(2\sqrt{11}\right)^{2}$$

The square of \sqrt{5} is 5.

$$16\times 5-\left(2\sqrt{11}\right)^{2}$$

Multiply 16 and 5 to get 80.

$$80-\left(2\sqrt{11}\right)^{2}$$

Expand \left(2\sqrt{11}\right)^{2}.

$$80-2^{2}\left(\sqrt{11}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$80-4\left(\sqrt{11}\right)^{2}$$

The square of \sqrt{11} is 11.

$$80-4\times 11$$

Multiply 4 and 11 to get 44.

$$80-44$$

Subtract 44 from 80 to get 36.

$$36$$

Factor

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