document.write( "Question 183083This question is from textbook algbra 2
\n" ); document.write( ": (x-3y)^6 i need to wirte this as a binomal expansion using pascal triangle \n" ); document.write( "
Algebra.Com's Answer #137455 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"%28x-3y%29%5E6\" 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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1   6   15   20   15   6   1   
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\n" ); document.write( "\n" ); document.write( "Looking at the row that starts with 1,6, etc, we can see that this row has the numbers:\r
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\n" ); document.write( "\n" ); document.write( "1, 6, 15, 20, 15, 6, 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 \"%28x-3y%29%5E6\", simply follow this procedure:\r
\n" ); document.write( "\n" ); document.write( "Write the first coefficient. Multiply that coefficient with the first binomial term \"x\" and then the second binomial term \"-3y\". 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%28x%29%28-3y%29\", raise \"x\" to the 6th power and raise \"-3y\" to the 0th power.\r
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\n" ); document.write( "\n" ); document.write( " Looking at the second term \"6%28x%29%28-3y%29\" raise \"x\" to the 5th power and raise \"-3y\" 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 \"x\" are stepping down and the exponents of \"-3y\" 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( "\"x%5E6-18x%5E5y%2B135x%5E4y%5E2-540x%5E3y%5E3%2B1215x%5E2y%5E4-1458xy%5E5%2B729y%5E6\" Multiply the terms with their coefficients\r
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\n" ); document.write( "\n" ); document.write( "So \"%28x-3y%29%5E6\" expands and simplifies to \"x%5E6-18x%5E5y%2B135x%5E4y%5E2-540x%5E3y%5E3%2B1215x%5E2y%5E4-1458xy%5E5%2B729y%5E6\".\r
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\n" ); document.write( "\n" ); document.write( "In other words, \n" ); document.write( "
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