Solve 36-2(3-2sqrt{2})(2sqrt{2}+3

$$36 - 2 ( 3 - 2 \sqrt { 2 } ) ( 2 \sqrt { 2 } + 3$$

Evaluate

$$34$$

Solution Steps

Multiply -1 and 2 to get -2.

$$36-2\left(3-2\sqrt{2}\right)\left(2\sqrt{2}+3\right)$$

Use the distributive property to multiply -2 by 3-2\sqrt{2}.

$$36+\left(-6+4\sqrt{2}\right)\left(2\sqrt{2}+3\right)$$

Apply the distributive property by multiplying each term of -6+4\sqrt{2} by each term of 2\sqrt{2}+3.

$$36-12\sqrt{2}-18+8\left(\sqrt{2}\right)^{2}+12\sqrt{2}$$

The square of \sqrt{2} is 2.

$$36-12\sqrt{2}-18+8\times 2+12\sqrt{2}$$

Multiply 8 and 2 to get 16.

$$36-12\sqrt{2}-18+16+12\sqrt{2}$$

Add -18 and 16 to get -2.

$$36-12\sqrt{2}-2+12\sqrt{2}$$

Combine -12\sqrt{2} and 12\sqrt{2} to get 0.

$$36-2$$

Subtract 2 from 36 to get 34.

$$34$$

Factor

$$2\times 17$$