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Problem 320

Algebra Difficulty 2.0 Find the answer CEMC Fermat

If x=2 x=2 , what is the value of (x+2−x)(2−x−2) (x+2-x)(2-x-2) ?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

When x=2 x=2 , we have (x+2−x)(2−x−2)=(2+2−2)(2−2−2)=(2)(−2)=−4 (x+2-x)(2-x-2)=(2+2-2)(2-2-2)=(2)(-2)=-4 . Alternatively, we could simplify (x+2−x)(2−x−2) (x+2-x)(2-x-2) to obtain (2)(−x) (2)(-x) or −2x -2x and then substitute x=2 x=2 to obtain a result of −2(2) -2(2) or -4.

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