Solve [(sqrt{7}+sqrt{5})-(sqrt{7}-sqrt{5})]^2

$$[ ( \sqrt { 7 } + \sqrt { 5 } ) - ( \sqrt { 7 } - \sqrt { 5 } ) ] ^ { 2 }$$

Evaluate

$$20$$

Solution Steps

To find the opposite of \sqrt{7}-\sqrt{5}, find the opposite of each term.

$$\left(\sqrt{7}+\sqrt{5}-\sqrt{7}+\sqrt{5}\right)^{2}$$

Combine \sqrt{7} and -\sqrt{7} to get 0.

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

Combine \sqrt{5} and \sqrt{5} to get 2\sqrt{5}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{5} is 5.

$$4\times 5$$

Multiply 4 and 5 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$