Problem:
What is the value of the following expression?
702−1121002−72⋅(100−7)(100+7)(70−11)(70+11)
Answer Choices:
A. 1
B. 99509951
C. 47794780
D. 107108
E. 8081
Solution:
Using difference of squares to factor the left term, we get
702−1121002−72⋅(100−7)(100+7)(70−11)(70+11)= (70−11)(70+11)(100−7)(100+7)⋅(100−7)(100+7)(70−11)(70+11)
Cancelling all the terms, we get (A)1 as the answer.
The problems on this page are the property of the MAA's American Mathematics Competitions