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 most appropriate option.
A) 54 B) 63 C) 75 D) 86 E) 98
(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.   63 = 7*9, so this is a possible value for the original expression.   The answer is 63.
<result>B</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)?