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CEMC Fermat, 2014

Algebra Difficulty 1.1 Junior Find the answer Canada

If x=2x=2, then (x+2−x)(2−x−2)(x+2-x)(2-x-2) equals

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Solution

When x=2x=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=2x=2 to obtain a result of −2(2)-2(2) or −4-4.

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