document.write( "Question 1203588: what is the coefficient of the 5th term of the expansion of (2x^2 + 3y^3)^10 how about the sum of exponents of the terms in expansion\r
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Algebra.Com's Answer #839266 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "It is not clear what you are asking when, at the end of your post, you say \"how about the sum of exponents of the terms in expansion\"....

\n" ); document.write( "The first term of the expansion is $\"%282x%5E2%29%5E10\"$ , so the exponent on that term is 2*10 = 20.

\n" ); document.write( "The second term includes factors of $\"%282x%5E2%29%5E9\"$ and $\"%283x%5E3%29%5E1\"$ , so the exponent on that term is (2*9)+(3*1) = 21.

\n" ); document.write( "On the next terms the sums of the exponents will be 22, then 23, then 24...

\n" ); document.write( "The last term is $\"%283y%5E3%29%5E10\"$ , so the exponent on that term is 3*10 = 30.

\n" ); document.write( "So the sums of the exponents on successive terms of the expansion will be 20, 21, 22, ..., and 30.

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