Determining Coefficients (Binomial Theorem Help) (1 Viewer)

alussovsky · Sep 8, 2019

So from what I've learnt so far, you almost always have to find the general term first before finding out the coefficient of a term in binomial. I understand how to do these for normal $(a+b)^x$ expansions, but how do you go about finding the general terms of binomial expansions that have more than one bracket? Sorry for the probably incorrect terminology, lol.

For example, how would you go about finding the general term of $(3+x)(1-x)^{15}$ for the coefficient of $x^4$ or $(2-5x+x^2)(1+x)^{11}$ for the coefficient of $x^9$ ?

For the first, I managed to get to $-(3+x)(\binom{15}{k}x^k)$ but I'm not sure how to progress from there to make a single $x^y$ and equate that to the required coefficient term. Unless that's the completely wrong way to go about it...? Well anyway, thanks!

Drongoski · Sep 8, 2019

The term in $x^9$ comes from combining (adding up) the product of 2 and the term in $x^9$ in the expansion of $(1+x)^{11}$ , the product of -5x and the term in $x^8$ and the product of $x^2$ and the term in $x^7$ .

alussovsky · Sep 8, 2019

Drongoski said:
The term in $x^9$ comes from combining (adding up) the product of 2 and the term in $x^9$ in the expansion of $(1+x)^{11}$ , the product of -5x and the term in $x^8$ and the product of $x^2$ and the term in $x^7$ .

Ah.. so I did do it the wrong way anyway, haha. Thanks!

Determining Coefficients (Binomial Theorem Help) (1 Viewer)

alussovsky

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Drongoski

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alussovsky

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