simple but vexing, evaluating algebraic expressions: a = 4 b = -3 a – b^2

unclematt3

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Nov 3, 2018
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simple but vexing, evaluating algebraic expressions: a = 4 b = -3 a – b^2

Scratching my head on this one.
a = 4 b = -3

a – b2

I maintain that the way to solve this is
(4) – (-3)2
4 – (9)
-5

My colleague says the following is correct
(4) – (-3)2
4 + 32
13

Please let me know what is the right answer, my way or my colleague's way.

Thank you!
 

Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,462
Scratching my head on this one.
a = 4 b = -3

a – b2

I maintain that the way to solve this is
(4) – (-3)2
4 – (9)
-5

My colleague says the following is correct
(4) – (-3)2
4 + 32
13

Please let me know what is the right answer, my way or my colleague's way.

Thank you!
Your answer is correct!!
 

mmm4444bot

Super Moderator
Staff member
Joined
Oct 6, 2005
Messages
10,324
Here's one way to explain the mistake, to your colleague. When we square a negative number, the "negative part" gets squared, too. (The negative sign in -3 represents a factor of -1.)

In other words:

-3 = (-1)(3)

Therefore:

(-3)^2 = (-1)^2 ∙ (3)^2 = (1)(9) = 9

This is why all squares are non-negative numbers. So, subtracting b^2 means subtracting positive 9, like you did. :cool:
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
4,142
Scratching my head on this one.
a = 4 b = -3

a – b2

I maintain that the way to solve this is
(4) – (-3)2
4 – (9)
-5

My colleague says the following is correct
(4) – (-3)2
4 + 32
13

Please let me know what is the right answer, my way or my colleague's way.

Thank you!
You didn't state how your colleague was thinking, but possibly he saw two negatives in a row and thought they cancel, as they would in 4 - (-3). The trouble here is that in between them, logically, there is a squaring, which changes the sign. Ultimately, this would be an "order of operations" issue.
 
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