2008 CEMC Gauss (Grade 8) Problems/Problem 4: Difference between revisions
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) }..." |
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{{CEMC box|year=2008|competition=Gauss (Grade 8)|num-b=3|num-a=5}} | |||
Latest revision as of 12:32, 20 October 2025
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
| 2008 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
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| CEMC Gauss (Grade 8) | ||
