Solve {left(4sqrt{10}right)}^2-{left(18sqrt{2}right)}^2

$${ \left(4 \sqrt{ 10 } \right) }^{ 2 } - { \left(18 \sqrt{ 2 } \right) }^{ 2 }$$

Evaluate

$$-488$$

Solution Steps

Expand \left(4\sqrt{10}\right)^{2}.

$$4^{2}\left(\sqrt{10}\right)^{2}-\left(18\sqrt{2}\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16\left(\sqrt{10}\right)^{2}-\left(18\sqrt{2}\right)^{2}$$

The square of \sqrt{10} is 10.

$$16\times 10-\left(18\sqrt{2}\right)^{2}$$

Multiply 16 and 10 to get 160.

$$160-\left(18\sqrt{2}\right)^{2}$$

Expand \left(18\sqrt{2}\right)^{2}.

$$160-18^{2}\left(\sqrt{2}\right)^{2}$$

Calculate 18 to the power of 2 and get 324.

$$160-324\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$160-324\times 2$$

Multiply 324 and 2 to get 648.

$$160-648$$

Subtract 648 from 160 to get -488.

$$-488$$

Factor

$$-488$$