Maths Olympiad Prep

Library / /19 of 165

Algebra Difficulty 2.0 Junior Find the answer

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.

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.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.