Solve (3sqrt{5})^2-(5sqrt{3})^2

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

Evaluate

$$-30$$

Solution Steps

Expand \left(3\sqrt{5}\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{5}\right)^{2}-\left(5\sqrt{3}\right)^{2}$$

The square of \sqrt{5} is 5.

$$9\times 5-\left(5\sqrt{3}\right)^{2}$$

Multiply 9 and 5 to get 45.

$$45-\left(5\sqrt{3}\right)^{2}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$45-5^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$45-25\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$45-25\times 3$$

Multiply 25 and 3 to get 75.

$$45-75$$

Subtract 75 from 45 to get -30.

$$-30$$

Factor

$$-30$$