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