document.write( "Question 281409: (a+b+c+d)4th power (I WANT THE FULL WORKING AND NOT JUST THE ANSWER WANT TO SEE HOW YOU DID IT) \n" ); document.write( "
Algebra.Com's Answer #204417 by Mathematicians(84)\"\" \"About 
You can put this solution on YOUR website!
This one is not that hard, it is just very tedious. Basically,\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "The way I am going to go through this problem is multiply the first and second together and then the same result should be the third and fourth multiplied together. Also, the key trick to doing this is to know how to multiply these together. You have to do something like distributing and foiling. \r
\n" ); document.write( "\n" ); document.write( "Let (a+b) = R and let c + d = S\r
\n" ); document.write( "\n" ); document.write( "Then (a+b+c+d) = R + S\r
\n" ); document.write( "\n" ); document.write( "Instead of \"%28a+%2B+b+%2B+c+%2B+d%29%5E4\" we can do \"%28R+%2B+S%29%5E4\" and make the substitutions.\r
\n" ); document.write( "\n" ); document.write( "\"%28R%2BS%29%28R%2BS%29%28R%2BS%29%28R%2BS%29+=+%28R%2BS%29%5E2+%2A+%28R%2BS%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"+%28R%2BS%29%5E2+=+%28R%5E2+%2B+RS+%2B+SR+%2B+S%5E2%29+=+R%5E2+%2B+2RS+%2B+S%5E2+\" Using foiling.\r
\n" ); document.write( "\n" ); document.write( "Then \r
\n" ); document.write( "\n" ); document.write( "When combing like terms we get:\r
\n" ); document.write( "\n" ); document.write( "\"%28R%2BS%29%5E4+=+R%5E4+%2B+4R%5E3S+%2B+6R%5E2S%5E2+%2B+4RS%5E3+%2B+S%5E4\"\r
\n" ); document.write( "\n" ); document.write( "However, we want out answers in a,b,c,d so we need to resubstitute them back in.\r
\n" ); document.write( "\n" ); document.write( "\"R+=+%28a+%2B+b%29\" and \"S+=+%28c+%2B+d%29\"\r
\n" ); document.write( "\n" ); document.write( "so we get:\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "Right now it seems like a lot of the work, but (R+S)^4 is the same as (a + b)^4 except different lettering and we already did (R+S)^4 so:\r
\n" ); document.write( "\n" ); document.write( "also, (after combining like terms.\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "Almost the fun part, but we still have more distributing to do and everything:\r
\n" ); document.write( "\n" ); document.write( "so I am going to break this up into five parts:
\n" ); document.write( "\"%28a%5E4+%2B+4a%5E3b+%2B+6a%5E2b%5E2+%2B+4ab%5E3+%2B+b%5E4%29\" (no work needs to be done)\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( " is the same thing as part 2 but a switched with c and b switched with d.
\n" ); document.write( "= \r
\n" ); document.write( "\n" ); document.write( "\"%28c%5E4+%2B+4c%5E3d+%2B+6c%5E2d%5E2+%2B+4cd%5E3+%2B+d%5E4%29\" (no work needs to be done)\r
\n" ); document.write( "\n" ); document.write( "Now we add them up! The fun part! Remember you can only combine like terms if they have the same variables with the same exponents.\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "I hope that is the right answer, a lot of it was calculating in my head! Hope this helps! \n" ); document.write( "
\n" );