document.write( "Question 77049This question is from textbook Glencoe Algebra 1
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Algebra.Com's Answer #55220 by bucky(2189) $\"\"$ $\"About$

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$\"n%5E3-81n=0\"$
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\n" ); document.write( "Notice that both terms on the left side contain the common factor n. Factor it out to
\n" ); document.write( "get:
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\n" ); document.write( " $\"n%2A%28n%5E2-81%29=0\"$
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\n" ); document.write( "Next notice that the expression within the parentheses is in the form of the difference
\n" ); document.write( "of two squares. This is a common form that can be factored according to the following
\n" ); document.write( "rule:
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\n" ); document.write( " $\"%28a%5E2+-+b%5E2%29+=+%28a%2Bb%29%2A%28a-b%29\"$
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\n" ); document.write( "Applying this rule to $\"%28n%5E2-81%29\"$ results in the factors $\"%28n%2B9%29%2A%28n-9%29\"$ . Substituting this
\n" ); document.write( "into our first factor changes it to:
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\n" ); document.write( " $\"n%2A%28n%5E2-81%29+=+n%2A%28n%2B9%29%2A%28n-9%29+=+0\"$
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\n" ); document.write( "This equation will be true if any of the three factors on the left side equal zero. Therefore,
\n" ); document.write( "set each of the factors equal to zero and solve for the corresponding value of n, and the
\n" ); document.write( "resulting three values of n will make the equation correct.
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\n" ); document.write( "First, let $\"n+=+0\"$ . No solving is necessary. This tells you immediately one value of n
\n" ); document.write( "that will cause the original equation of $\"n%5E3-81n=0\"$ to become 0 = 0.
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\n" ); document.write( "Next, let $\"n%2B9+=0\"$ . Subtract 9 from both sides of the equation, and the resulting
\n" ); document.write( "equation is $\"n+=+-9\"$ . This tells you that if you let n = -9 in the original equation,
\n" ); document.write( "the original equation of $\"n%5E3-81n=0\"$ will become 0 = 0.
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\n" ); document.write( "Finally, let $\"n+-9+=+0\"$ . Add 9 to both sides of this equation and the resulting
\n" ); document.write( "equation is $\"n+=+9\"$ . If you let n = +9 in the original equation, the original equation
\n" ); document.write( "of $\"n%5E3-81n=0\"$ will become 0 = 0.
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\n" ); document.write( "So the solutions to the original problem are n = 0, n = -9, and n= +9.
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\n" ); document.write( "Hope this helps and shows you a way that you can solve for equations that can be factored.\r
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