If a = 7 and b = -7, what is the value of 2a - 2b + b^2 ?

Given: \(a = 7\) and \(b = -7\)

Asked: What is the value of \(2a - 2b + b^2\) ?

2(7) - 2(-7) + (-7)^2
= 14 + 14 + 49 = 77

IMO E

The question is easy enough, and substituting the values would be sufficient and the best way in this case to get to the answer.

If there were more terms or if the values were so big that substitution would involve too much calculation, then we might try to get to the answer by eliminating options.


(a) The first elimination point could be to see if \(2a - 2b + b^2\) is Odd or Even. In this case since all the options are Odd, we do not need to check the same.



(b) We know that 2a is positive, -2b is also positiveve (since b = -7) and \(b^2\) will always be positive.

\(2a - 2b + b^2\) is positiveve and hence Option A is ruled out.



(c) Since 2(a - b) = 2(a - b) is positive and \(b^2\) = 49, Options B and C are eliminated (as they have to be greater than 49.



(d) a - b = 7 - (-7) = 14 and 14 + 49 = 63. Option D gets ruled without having to multiply by 2 as the answer has to be greater than 63.


Option E would be the correct choice.

Arun Kumar

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