If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?
Choose the correct choice
A) 35
B) 45
C) 55
D) 65
E) 75
(a^2-b^2)(b^2-c^2) = (a+b)*(a-b)*(b+c)*(b-c) = (a+b)*(-1)*(b+c)*(-1) = (a+b)*(b+c)   Therefore, the product should have factors with a difference of 2.   35 = 5*7, so this is a possible value for the original expression.   The answer is 35.
<result>A</result>
If a,b, and c are consecutive positive integers and a>b>c, what can be the value of (a^2-b^2)(b^2-c^2)?