document.write( "Question 271416: simplify\r
\n" ); document.write( "\n" ); document.write( "-√x^2+4x+4 \n" ); document.write( "

Algebra.Com's Answer #199207 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
If your problem is not
\n" ); document.write( " $\"-sqrt%28x%5E2%2B4x%2B4%29\"$
\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 $\"x%5E2%2B4x%2B4\"$ fits the pattern $\"a%5E2+%2B2ab+%2B+b%5E2+=+%28a%2Bb%29%5E2\"$ with a = x and b = 2. So our expression can be rewritten as:
\n" ); document.write( " $\"-sqrt%28%28x%2B2%29%5E2%29\"$
\n" ); document.write( "Now we have the square root of a perfect square! The easy mistake to make here is to think that $\"sqrt%28%28x%2B2%29%5E2%29+=+x%2B2\"$ . But a square root is supposed to positive. And x+2 may not be positive. So we use absolute value to ensure a positive square root:
\n" ); document.write( " $\"-abs%28x%2B2%29\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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