document.write( "Question 271414: simplify
\n" ); document.write( " -√4a^2+4a+1 \n" ); document.write( "

Algebra.Com's Answer #199205 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
If your problem is not
\n" ); document.write( " $\"-sqrt%284a%5E2%2B4a%2B1%29\"$
\n" ); document.write( "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.

\n" ); document.write( "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:
\n" ); document.write( " $\"-sqrt%28%282a%2B1%29%5E2%29\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"-abs%282a%2B1%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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