document.write( "Question 715608: I need help with this question. What is the third term in the expansion of (x + 2y) power of 17? \n" ); document.write( "

Algebra.Com's Answer #439530 by KMST(5328) $\"\"$ $\"About$

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SInce the power is $\"17\"$ , the expansion would have $\"17%2B1=18\"$ terms.
\n" ); document.write( "The degree of all the terms (the sum of the powers of $\"x\"$ and of $\"%282y%29\"$ ) will be $\"17\"$ .
\n" ); document.write( "The first term will have $\"x%5E17\"$ and $\"%282y%29%5E0\"$ .
\n" ); document.write( "The second term will have $\"x%5E16\"$ and $\"%282y%29%5E1\"$ .
\n" ); document.write( "Term number $\"3\"$ would have
\n" ); document.write( " $\"%282y%29%5E%28%283-1%29%29=%282y%29%5E2=4y%5E2\"$ as a factor.
\n" ); document.write( "As the power is $\"17\"$ , it would also have
\n" ); document.write( " $\"x%5E%28%2817-2%29%29=x%5E15\"$ as a factor.
\n" ); document.write( "The other factor would be the combinatorial number that tells you how many different groups of 2 you can make with 17 different items:
\n" ); document.write( " $\"%28matrix%282%2C1%2C17%2C2%29%29=17%2A16%2F1%2F2=136\"$
\n" ); document.write( "The third term is
\n" ); document.write( " $\"136%2Ax%5E15%2A4y%5E2=highlight%28544x%5E15y%5E2%29\"$ \n" ); document.write( "

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