Solve (32+2(-18+4sqrt{34}))(40+2(-18+4sqrt{34}))-720=

$$(32+2(-18+4 \sqrt{ 34 } ))(40+2(-18+4 \sqrt{ 34 } ))-720=$$

Evaluate

$$1440$$

Solution Steps

Use the distributive property to multiply 2 by -18+4\sqrt{34}.

$$\left(32-36+8\sqrt{34}\right)\left(40+2\left(-18+4\sqrt{34}\right)\right)-720$$

Subtract 36 from 32 to get -4.

$$\left(-4+8\sqrt{34}\right)\left(40+2\left(-18+4\sqrt{34}\right)\right)-720$$

Use the distributive property to multiply 2 by -18+4\sqrt{34}.

$$\left(-4+8\sqrt{34}\right)\left(40-36+8\sqrt{34}\right)-720$$

Subtract 36 from 40 to get 4.

$$\left(-4+8\sqrt{34}\right)\left(4+8\sqrt{34}\right)-720$$

Apply the distributive property by multiplying each term of -4+8\sqrt{34} by each term of 4+8\sqrt{34}.

$$-16-32\sqrt{34}+32\sqrt{34}+64\left(\sqrt{34}\right)^{2}-720$$

Combine -32\sqrt{34} and 32\sqrt{34} to get 0.

$$-16+64\left(\sqrt{34}\right)^{2}-720$$

The square of \sqrt{34} is 34.

$$-16+64\times 34-720$$

Multiply 64 and 34 to get 2176.

$$-16+2176-720$$

Add -16 and 2176 to get 2160.

$$2160-720$$

Subtract 720 from 2160 to get 1440.

$$1440$$

Factor

$$2^{5}\times 3^{2}\times 5$$