Question 1110359: Evaluating expression; in my text book there are two problems; #5) b=5, -b^2+b and #6) (-b)^2+b. Than book's answer for the first is -20; so 5 is squared then the negative is applied to get -25+5=20. The second problem would be (-5)^2+5=30. The point of the two problems is to show the first does not include the "-" sign in the squaring, whereas it is in the second.
The next problem is #7) a=-2; 3a^2. The book's answer is +12 3 times -2^2 including the "-" sign is squared to get +4. So according to illustration of the two previous problems, shouldn't it be written as 3(a)^2 which would be 3(-2)^2.
otherwise the notation is inconsistent.
Sorry, I asked a similar question but formed it int he wrong way. It was very late!
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! #5 says "square b, negate the result, then add b"
#6 says "negate b, square the result, then add b"
#7 says "square a, multiply the result by 3"
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There is no inconsistency in the notation.
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While it is not an error to write  , it is also not something you will see in general.
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Note that negation is the same as multiplying a number by -1, and so it occurs just like any other multiplication in the standard order of operations.
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To the student: read my response carefully. There is no inconsistency. You are confusing
(1) a minus sign appearing in an equation
with
(2) a variable taking on negative values
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Sure, in EVALUATING  for a=-2, one adds parenthesis  because without them, it would change the meaning of the expression. That's why I wrote out the meaning of each expression in words, and you should practice doing that. There is no "negation" here, the expression is being evaluated for a value of 'a' that is less than zero. Think of a number line, with zero at the middle. Numbers to the left of zero are negative, numbers to the right of zero are positive.
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Example 1
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y = -a <-—— means "y equals negative a" or equivalently, "y equals -1 times 'a' "
if a=-12, then y = -(-12) = (-1)*(-12) = 12
if a=64, then y = -64
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The "-" sign in the equation y=-a in example 1 is similar to that of problem #5, while the VALUE -12 corresponds to the -2 they gave you to plug in to problem #7.
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You are free to add parenthesis when it provides clarity. You are REQUIRED to add parenthesis if the meaning of the expression would otherwise be changed without them (see example 2).
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Example 2
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Many times on this site, students will ask questions such as "  , solve for x in terms of y" but sometimes they don't use the formatting brackets and instead write y = 3-x/2+5x. To convey the proper expression, they should add parenthesis y = (3-x)/(2+5x)
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EDITED 2/25: reworded very last sentence.
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