document.write( "Question 535715: name and describe two types of Special Products that you may be able quickly recognize and factor if found embedded within a rational expression? \n" ); document.write( "

Algebra.Com's Answer #351990 by KMST(5328) $\"\"$ $\"About$

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I would recognize the square of a binomial
\n" ); document.write( " $\"a%5E2%2B2ab%2Bb%5E2=%28a%2Bb%29%5E2\"$ and
\n" ); document.write( "a difference of squares
\n" ); document.write( " $\"a%5E2-b%5E2=%28a%2Bb%29%28a-b%29\"$
\n" ); document.write( "I would look for two monomials/terms that are perfect squares, such as
\n" ); document.write( " $\"4\"$ , $\"81x%5E2\"$ , $\"16x%5E4y%5E6\"$
\n" ); document.write( "If there is only two such monomials, and they have opposite signs, then I would see it as a difference of squares.
\n" ); document.write( "If there were two such monomials, with the same sign, and a third term, I would figure out if the third term is double the product of the square roots of the other two.
\n" ); document.write( "For example, in $\"36x-81x%5E2-4\"$
\n" ); document.write( "I recognize the perfect square terms $\"4\"$ , and $\"81x%5E2\"$ .
\n" ); document.write( "Since they both appear with a minus sign (same sign), I would calculate the square roots (of the monomials without the minus sign, of course), as
\n" ); document.write( " $\"2\"$ , and $\"9x\"$ .
\n" ); document.write( "Then I would calculate twice their product
\n" ); document.write( " $\"2%282%29%289x%29=36x\"$
\n" ); document.write( "Since it equals the third term, the factoring is
\n" ); document.write( " $\"36x-81x%5E2-4=%28-1%29%2881x%5E2-36x%2B4%29=%28-1%29%289x-2%29%5E2\"$ \n" ); document.write( "

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