Solve (-1)(1+sqrt{2})quad(16)(2-sqrt{8})

$$( - 1 ) ( 1 + \sqrt { 2 } ) \quad ( 16 ) ( 2 - \sqrt { 8 } )$$

Evaluate

$$32$$

Solution Steps

Multiply -1 and 16 to get -16.

$$-16\left(1+\sqrt{2}\right)\left(2-\sqrt{8}\right)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-16\left(1+\sqrt{2}\right)\left(2-2\sqrt{2}\right)$$

Use the distributive property to multiply -16 by 1+\sqrt{2}.

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

Apply the distributive property by multiplying each term of -16-16\sqrt{2} by each term of 2-2\sqrt{2}.

$$-32+32\sqrt{2}-32\sqrt{2}+32\left(\sqrt{2}\right)^{2}$$

Combine 32\sqrt{2} and -32\sqrt{2} to get 0.

$$-32+32\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$-32+32\times 2$$

Multiply 32 and 2 to get 64.

$$-32+64$$

Add -32 and 64 to get 32.

$$32$$

Factor

$$2^{5}$$