document.write( "Question 711099: Find the indicated product. (2x+5)^3 \n" ); document.write( "
Algebra.Com's Answer #437289 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
\"%282x%2B5%29%5E3\"
\n" ); document.write( "There are several ways to find this product:
  • Rewrite it as (2x+5)(2x+5)(2x+5) and then multiply it out by hand. (The first multiplication can be done with FOIL (or the \"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\" pattern). But when you multiply that by the third (2x+5) you will have to use the general way to multiply polynomials: Multiply each term of one factor by each term of the other factor and then add like terms, if any.)
  • Use the Binomial Theorem, if you know it, which provides a formula for \"%28a%2Bb%29%5En\". In this case we would use 3 for the \"n\".
  • Most students are expected to learn the binomial square pattern: \"%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2\". Fewer students go beyond this to memorize the pattern for the cube of a binomial. If you happen to know this pattern, this would be the easiest way to get to the answer.
I'm going to assume that you do not know the last two methods (which are shorter than the first). So I will multiply this out by hand.

\n" ); document.write( "\"%282x%2B5%29%282x%2B5%29%282x%2B5%29\"
\n" ); document.write( "I will, however, take advantage of the binomial square pattern to do the first multiplication:
\n" ); document.write( "\"%28%282x%29%5E2+%2B2%282x%29%285%29%2B%285%29%5E2%29%282x%2B5%29\"
\n" ); document.write( "which simplifies to:
\n" ); document.write( "\"%284x%5E2+%2B20x%2B25%29%282x%2B5%29\"

\n" ); document.write( "Now we do the second multiplication:
\n" ); document.write( "\"4x%5E2%2A2x%2B4x%5E2%2A5%2B20x%2A2x%2B20x%2A5%2B25%2A2x%2B25%2A5\"
\n" ); document.write( "which simplifies as follows:
\n" ); document.write( "\"8x%5E3%2B20x%5E2%2B40x%5E2%2B100x%2B50x%2B125\"
\n" ); document.write( "\"8x%5E3%2B60x%5E2%2B150x%2B125\"

\n" ); document.write( "P.S. If you're curious, the pattern for a binomial cube is:
\n" ); document.write( "\"%28a%2Bb%29%5E3+=+a%5E3+%2B+3a%5E2b+%2B+3ab%5E2+%2B+b%5E3\"
\n" ); document.write( "Using this pattern on your expression, with the \"a\" being \"2x\" and the \"b\" being \"5\", we get:
\n" ); document.write( "\"%282x%29%5E3+%2B+3%282x%29%5E2%285%29+%2B+3%282x%29%285%29%5E2+%2B+%285%29%5E3\"
\n" ); document.write( "Simplifying:
\n" ); document.write( "\"8x%5E3+%2B+3%284x%5E2%29%285%29+%2B+3%282x%29%2825%29+%2B+125\"
\n" ); document.write( "\"8x%5E3+%2B+60x%5E2+%2B+150x+%2B+125\" \n" ); document.write( "
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