document.write( "Question 1187142: Find the coefficient of x^22 in the expansion of (1-3x)(1+x^3)^10. \n" ); document.write( "

Algebra.Com's Answer #818342 by KMST(5328) $\"\"$ $\"About$

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The expansion of $\"%28y%2B1%29%5E10\"$ is
\n" ); document.write( " $\"%28y%2B1%29%5E10=y%5E10=10y%5E9%2B45y%5E8%2B120y%5E7%2B210y%5E6%2B%22...%22\"$ where the coefficient of $\"y%5E7\"$ is $\"10%2A9%2A8%2F%283%2A2%29=120\"$ .
\n" ); document.write( "With $\"x%5E3=y\"$ it is
\n" ); document.write( " $\"%28x%5E3%2B1%29%5E10=x%5E30=10x%5E27%2B45x%5E24%2B120x%5E21%2B210x%5E18%2B%22...%22\"$
\n" ); document.write( "When that is multiplied times $\"%281-3x%29\"$ the term in $\"x%5E22\"$ will be
\n" ); document.write( " $\"%28-3x%29%28120x%5E21%29=-360x%5E22\"$
\n" ); document.write( "The coefficient of $\"x%5E22\"$ is $\"highlight%28-360%29\"$ . \n" ); document.write( "

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