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

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

Evaluate

$$-76$$

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}.

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Calculate 4 to the power of 2 and get 16.

$$4-16\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$4-16\times 5$$

Multiply 16 and 5 to get 80.

$$4-80$$

Subtract 80 from 4 to get -76.

$$-76$$

Factor

$$-76$$