Binomial Expansion

Daniel123 · 2007-09-20 05:33:14

My teacher went through an example today... but there is a part of it that I don't understand.

The coefficient of x³ in the expansion (2 + x)(3 - ax)^4 is 30. Find the values of the constant, a.

It is this part that I don't understand. I can see that multiplying the x² term by x will give you x³, but when the x³ term is multiplid by 2, wouldn't it be multiplied by x as well? therefore making it x^4? (and the x² term would also be multiplied by 2).

At this point, we haven't learned how to solve cubics yet, so the final answer doesn't matter.

Ricky · 2007-09-20 07:45:16

I take it you have yet to go over binomial theorem?

Daniel123 · 2007-09-20 07:50:23

I have... I'm just unsure about that part :S

mathsyperson · 2007-09-20 08:06:14

Daniel123 wrote:

It is this part that I don't understand. I can see that multiplying the x² term by x will give you x³, but when the x³ term is multiplid by 2, wouldn't it be multiplied by x as well?

Nope. 2 is a constant, so the power of x is unaffected.

adam_dsutton · 2007-09-20 08:11:33

:)

Daniel123 · 2007-09-20 09:53:29

I don't think I've made myself clear.

when the expanded bracket is multiplied by (2 + x), wouldn't the (-ax)³ become -ax^4?

mathsyperson · 2007-09-20 10:03:29

Partially.

The -ax³ term is multiplied by (2+x), which gives -2ax³ -ax[sup]4[/sup].
However, the question is only interested in the x³ coefficient, so the x[sup]4[/sup] part is ignored.

Last edited by mathsyperson (2007-09-21 03:12:42)

Daniel123 · 2007-09-21 02:52:52

ohh ok.

thank you.

Math Is Fun Forum

#1 2007-09-20 05:33:14

Binomial Expansion

#2 2007-09-20 07:45:16

Re: Binomial Expansion

#3 2007-09-20 07:50:23

Re: Binomial Expansion

#4 2007-09-20 08:06:14

Re: Binomial Expansion

#5 2007-09-20 08:11:33

Re: Binomial Expansion

#6 2007-09-20 09:53:29

Re: Binomial Expansion

#7 2007-09-20 10:03:29

Re: Binomial Expansion

#8 2007-09-21 02:52:52

Re: Binomial Expansion

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