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

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

Evaluate

$$-116$$

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}.

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

Calculate 3 to the power of 2 and get 9.

$$9-\left(5\sqrt{5}\right)^{2}$$

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

$$9-5^{2}\left(\sqrt{5}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$9-25\left(\sqrt{5}\right)^{2}$$

The square of \sqrt{5} is 5.

$$9-25\times 5$$

Multiply 25 and 5 to get 125.

$$9-125$$

Subtract 125 from 9 to get -116.

$$-116$$

Factor

$$-116$$