2008 CEMC Gauss (Grade 8) Problems/Problem 4
Revision as of 12:20, 1 October 2025 by Anabel.disher (talk | contribs) (Created page with "==Problem== The value of <math>(1 + 2)^2 - (1^2 + 2^2)</math> is <math> \text{ (A) }\ 14 \qquad\text{ (B) }\ 4 \qquad\text{ (C) }\ 2 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }...")
Problem
The value of 
is
Solution 1
Using order of operations, we get:
~anabel.disher
Solution 2
We can notice that 
.
We can now plug in 
for 
and 
for 
to get:
~anabel.disher
Solution 3 (answer choices)
Since 
and all of the numbers involved in the equation are integers, we can notice that the number must be a perfect square after adding 
.
, 
, 
, 
, and 
Of these numbers, the only number that was a perfect square after adding was 
~anabel.disher
