document.write( "Question 75663: (r+4)^4 I need help solving this one. \r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "
Algebra.Com's Answer #54348 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
You could write this as
\n" ); document.write( "\"%28r%2B4%29%28r%2B4%29%28r%2B4%29%28r%2B4%29\" and multiply this out the long way, but there is a much faster way to tackle these sort of problems. We're going to use Binomial Expansion to expand this term. The general rule to expand \"%28a%2Bb%29%5En\" is that we start out with \"c%2Aa%5En%2Ab%5E0\" and for each term we decrement n for a and increment the exponent for b so the 2nd terms looks like \"c%2Aa%5E%28n-1%29b%5E1\" until we get to \"c%2Aa%5E0b%5En\" for our last term. The coefficient (c) that is placed in front of each term is found in Pascal's triangle. So for \"%28a%2Bb%29%5E4\" we need to look at the row containing:\r
\n" ); document.write( "\n" ); document.write( "1,4,6,4,1\r
\n" ); document.write( "\n" ); document.write( "And these coefficients are placed in front of the variables. So if we have
\n" ); document.write( "\"%28r%2B4%29%5E4\" it becomes
\n" ); document.write( " Notice the terms in the parenthesis are the coefficients
\n" ); document.write( "\"r%5E4%2B4%2A4r%5E3%2B6%2A16r%5E2%2B4%2A64r%2B256\"
\n" ); document.write( "\"r%5E4%2B16r%5E3%2B96r%5E2%2B256r%2B256\"
\n" ); document.write( "Hope this makes sense. If not just look at row containing
\n" ); document.write( "1,2,1
\n" ); document.write( "This is the row of coefficients that are appended to the expansion of
\n" ); document.write( "\"%28a%2Bb%29%5E2\"
\n" ); document.write( "which expands to:
\n" ); document.write( "\"a%5E2%2B2ab%2Bb%5E2\"
\n" ); document.write( "which can be written as:
\n" ); document.write( "\"%281%29a%5E2%2Ab%5E0%2B%282%29a%5E1b%5E1%2B%281%29a%5E0b%5E2\"
\n" ); document.write( "and you can see the coefficients from the triangle in the parenthesis. \n" ); document.write( "
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