Solve (4-8sqrt{2})*(-1+2sqrt{2})

$$(4-8 \sqrt{ 2 } ) \times (-1+2 \sqrt{ 2 } )$$

Evaluate

$$16\sqrt{2}-36\approx -13.372583002$$

Solution Steps

Apply the distributive property by multiplying each term of 4-8\sqrt{2} by each term of -1+2\sqrt{2}.

$$-4+8\sqrt{2}+8\sqrt{2}-16\left(\sqrt{2}\right)^{2}$$

Combine 8\sqrt{2} and 8\sqrt{2} to get 16\sqrt{2}.

$$-4+16\sqrt{2}-16\left(\sqrt{2}\right)^{2}$$

The square of \sqrt{2} is 2.

$$-4+16\sqrt{2}-16\times 2$$

Multiply -16 and 2 to get -32.

$$-4+16\sqrt{2}-32$$

Subtract 32 from -4 to get -36.

$$-36+16\sqrt{2}$$

Factor

$$4 {(4 \sqrt{2} - 9)} = -13.372583002$$