Solve left(sqrt{3}-2right)2007*left(2+sqrt{3}right)2008

$$\left( \sqrt{ 3 } -2 \right) 2007 \times \left( 2+ \sqrt{ 3 } \right) 2008$$

Evaluate

$$-4030056$$

Solution Steps

Multiply 2007 and 2008 to get 4030056.

$$4030056\left(\sqrt{3}-2\right)\left(2+\sqrt{3}\right)$$

Use the distributive property to multiply 4030056 by \sqrt{3}-2.

$$\left(4030056\sqrt{3}-8060112\right)\left(2+\sqrt{3}\right)$$

Apply the distributive property by multiplying each term of 4030056\sqrt{3}-8060112 by each term of 2+\sqrt{3}.

$$8060112\sqrt{3}+4030056\left(\sqrt{3}\right)^{2}-16120224-8060112\sqrt{3}$$

The square of \sqrt{3} is 3.

$$8060112\sqrt{3}+4030056\times 3-16120224-8060112\sqrt{3}$$

Multiply 4030056 and 3 to get 12090168.

$$8060112\sqrt{3}[phone]-16120224-8060112\sqrt{3}$$

Subtract 16120224 from 12090168 to get -4030056.

$$8060112\sqrt{3}-4030056-8060112\sqrt{3}$$

Combine 8060112\sqrt{3} and -8060112\sqrt{3} to get 0.

$$-4030056$$

Factor

$$-4030056$$