document.write( "Question 183017This question is from textbook saxon algebra 2
\n" ); document.write( ": Use the Binomial Theorem to expand (3r-2)^5 \n" ); document.write( "
Algebra.Com's Answer #137392 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"%283r-2%29%5E5\" Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( "To expand this, we're going to use binomial expansion. So let's look at Pascal's triangle:
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1   

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1   1   

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1   2   1   

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1   3   3   1   

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1   4   6   4   1   

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1   5   10   10   5   1   
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\n" ); document.write( "\n" ); document.write( "Looking at the row that starts with 1,5, etc, we can see that this row has the numbers:\r
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\n" ); document.write( "\n" ); document.write( "1, 5, 10, 10, 5, and 1\r
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\n" ); document.write( "\n" ); document.write( "These numbers will be the coefficients of our expansion. So to expand \"%283r-2%29%5E5\", simply follow this procedure:\r
\n" ); document.write( "\n" ); document.write( "Write the first coefficient. Multiply that coefficient with the first binomial term \"3r\" and then the second binomial term \"-2\". Repeat this until all of the coefficients have been written.\r
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\n" ); document.write( "\n" ); document.write( "Once that has been done, add up the terms like this:\r
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\n" ); document.write( "\n" ); document.write( " Notice how the coefficients are in front of each term.\r
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\n" ); document.write( "\n" ); document.write( "However, we're not done yet.\r
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\n" ); document.write( "\n" ); document.write( " Looking at the first term \"1%283r%29%28-2%29\", raise \"3r\" to the 5th power and raise \"-2\" to the 0th power.\r
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\n" ); document.write( "\n" ); document.write( " Looking at the second term \"5%283r%29%28-2%29\" raise \"3r\" to the 4th power and raise \"-2\" to the 1st power.\r
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\n" ); document.write( "\n" ); document.write( "Continue this until you reach the final term.\r
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\n" ); document.write( "\n" ); document.write( "Notice how the exponents of \"3r\" are stepping down and the exponents of \"-2\" are stepping up.\r
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\n" ); document.write( "\n" ); document.write( "So the fully expanded expression should now look like this:\r
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\n" ); document.write( "\n" ); document.write( " Distribute the exponents\r
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\n" ); document.write( "\n" ); document.write( " Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"243r%5E5-810r%5E4%2B1080r%5E3-720r%5E2%2B240r-32\" Multiply the terms with their coefficients\r
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\n" ); document.write( "\n" ); document.write( "So \"%283r-2%29%5E5\" expands and simplifies to \"243r%5E5-810r%5E4%2B1080r%5E3-720r%5E2%2B240r-32\".\r
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\n" ); document.write( "\n" ); document.write( "In other words, \"%283r-2%29%5E5=243r%5E5-810r%5E4%2B1080r%5E3-720r%5E2%2B240r-32\" \n" ); document.write( "
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