Solve (2sqrt{5}+1)(1-2sqrt{5})

$$( 2 \sqrt { 5 } + 1 ) ( 1 - 2 \sqrt { 5 } )$$

Evaluate

$$-19$$

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}.

$$1^{2}-\left(2\sqrt{5}\right)^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1-\left(2\sqrt{5}\right)^{2}$$

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

$$1-2^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$1-4\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$1-4\times 5$$

Multiply 4 and 5 to get 20.

$$1-20$$

Subtract 20 from 1 to get -19.

$$-19$$

Factor

$$-19$$