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

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

Evaluate

$$32$$

Solution Steps

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

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

Calculate 5 to the power of 2 and get 25.

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

The square of \sqrt{2} is 2.

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

Multiply 25 and 2 to get 50.

$$50-\left(3\sqrt{2}\right)^{2}$$

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

$$50-3^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$50-9\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$50-9\times 2$$

Multiply 9 and 2 to get 18.

$$50-18$$

Subtract 18 from 50 to get 32.

$$32$$

Factor

$$2^{5}$$