SOLUTION: simplify -√4a^2+4a+1

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Question 271414: simplify
-√4a^2+4a+1
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
If your problem is not
-sqrt%284a%5E2%2B4a%2B1%29
then please repost your question and use parentheses around the expression that belongs inside the square root and use parentheses around the expression to which the "-" applies.

To simplify this expression, we need to recognize that 4a%5E2+%2B+4a+%2B+1 fits the pattern x%5E2+%2B2xy+%2B+y%5E2+=+%28x%2By%29%5E2 with x = 2a and y = 1. So our expression can be rewritten as:
-sqrt%28%282a%2B1%29%5E2%29
Now we have the square root of a perfect square! The easy mistake to make here is to think that sqrt%28%282a%2B1%29%5E2%29+=+2a%2B1. But a square root is supposed to positive. And 2a+1 may not be positive. So we use absolute value to ensure a positive square root:
-abs%282a%2B1%29