Solve (sqrt{2}+4sqrt{2})*(5sqrt{2}-7sqrt{2})

$$( \sqrt { 2 } + 4 \sqrt { 2 } ) \cdot ( 5 \sqrt { 2 } - 7 \sqrt { 2 } )$$

Evaluate

$$-20$$

Solution Steps

Combine \sqrt{2} and 4\sqrt{2} to get 5\sqrt{2}.

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

Combine 5\sqrt{2} and -7\sqrt{2} to get -2\sqrt{2}.

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

Multiply 5 and -2 to get -10.

$$-10\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$-10\times 2$$

Multiply -10 and 2 to get -20.

$$-20$$

Factor

$$-20$$