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January 16th, 2015, 02:15 PM   #1
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Coefficient find in expansion of a term

Hi

I just had this question.

What is the coefficient of the term x^18 in the expansion of (x^5+x^2+x)^10.

In the solve, they told to find the how x^18 can be formed with x^5, x^2 and x. Like

18= 2*5+8*1.........Now i understand why the sum should be 18 but why the summation of multiplier needs to be exactly 10 like the initial power?

Why we can not have 18=3*5+3*1????????????

Thanks in advance
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January 17th, 2015, 02:47 PM   #2
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Originally Posted by Shen View Post
Hi

I just had this question.

What is the coefficient of the term x^18 in the expansion of (x^5+x^2+x)^10.

In the solve, they told to find the how x^18 can be formed with x^5, x^2 and x. Like

18= 2*5+8*1.........Now i understand why the sum should be 18 but why the summation of multiplier needs to be exactly 10 like the initial power?

Why we can not have 18=3*5+3*1????????????

Thanks in advance
When you expand polynomials to a power, those (sum of powers = initial power) are the only terms you will get. Try binomial to see what happens.
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