document.write( "Question 774872: Determine whether the following trinomial is a perfect square. x^2 + 4x + 4 \n" ); document.write( "

Algebra.Com's Answer #472565 by KMST(5328) $\"\"$ $\"About$

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A trinomial could be the square of a binomial
\n" ); document.write( " $\"%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2\"$
\n" ); document.write( "(In words, the square of a binomial is the square of one term, plus the square of the other, plus their double product,
\n" ); document.write( "If we find two terms that are perfect squares, they could be the $\"a%5E2\"$ and $\"b%5E2\"$ in the \"formula\" above, and we would know what the $\"a\"$ and $\"b\"$ expressions are.
\n" ); document.write( "If it so happens the other term is twice the product of the $\"a\"$ and $\"b\"$ we figured out before, then the trinomial is a perfect square.
\n" ); document.write( "
\n" ); document.write( "In $\"x%5E2+%2B+4x+%2B+4\"$ , we find that
\n" ); document.write( " $\"x%5E2\"$ is the square of $\"red%28x%29\"$ , and
\n" ); document.write( " $\"4=2%2A2=2%5E2\"$ is the square of $\"blue%282%29\"$ .
\n" ); document.write( "We calculate twice the product of $\"red%28x%29\"$ and $\"blue%282%29\"$ as
\n" ); document.write( " $\"2%2Ablue%282%29%2Ared%28x%29=4x\"$ and it is equal to the other term.
\n" ); document.write( "So $\"x%5E2+%2B+4x+%2B+4=%28x%2B2%29%5E2\"$
\n" ); document.write( "It is a perfect square. \n" ); document.write( "

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