MathDB

49

Part of 1954 AMC 12/AHSME

Problems(1)

Difference of Squares

Source:

2/8/2009
The difference of the squares of two odd numbers is always divisible by 8 8. If a>b a>b, and 2a\plus{}1 and 2b\plus{}1 are the odd numbers, to prove the given statement we put the difference of the squares in the form: (A)\ (2a\plus{}1)^2\minus{}(2b\plus{}1)^2 \\ (B)\ 4a^2\minus{}4b^2\plus{}4a\minus{}4b \\ (C)\ 4[a(a\plus{}1)\minus{}b(b\plus{}1)] \\ (D)\ 4(a\minus{}b)(a\plus{}b\plus{}1) \\ (E)\ 4(a^2\plus{}a\minus{}b^2\minus{}b)