document.write( "Question 1158319: Explain how to find the fifth term of the expansion of (2x+3y)^9 without writing out the entire sequence. \n" ); document.write( "

Algebra.Com's Answer #781232 by Boreal(15235) $\"\"$ $\"About$

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From binomial expansion, the first part of the fifth term is 9C4. The (2x) is raised to the number of the term and the (3y) is raised to the complement (9-the number of the term, here 5). It looks like this below. The first term in the parentheses is raised to the progressively smaller power, and the second term Is raised to the progressively larger power.
\n" ); document.write( "
\n" ); document.write( "9C0(2x)^9*3y^0
\n" ); document.write( "9C1(2x)^8*3y^1
\n" ); document.write( "9C2(2x)^7*(3y)^2
\n" ); document.write( "9C3(2x)^6*(3y)^3 and
\n" ); document.write( "9C4(2x)^5*(3y)^4, which is one way to write it \n" ); document.write( "

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