Binomial question

Dell PC 2

17

I'm not quite sure why I'm not getting the term with x^3 correct.

(edited 11 months ago)

Reply 1

ghostwalker

17

Original post by Dell PC 2

I'm not quite sure why I'm not getting the term with x^3 correct.

In your last two terms, squaring and cubing.

You seem to think that

(a-b)^n = a^n-b^n

. Hopefully, you know the correct expansions.

(edited 11 months ago)

Reply 2

davros

16

Original post by Dell PC 2

I'm not quite sure why I'm not getting the term with x^3 correct.

As an additional comment, I really wouldn't take out a factor of 2 as you're introducing fractions and the possibility of error in your working. I'm sure you're aware of the binomial expansion in its simplest form where you can do (a + b)^n = ???, and in particular here just take a = 2 and b = "the other bit".

Reply 3

Dell PC 2

OP

17

Original post by ghostwalker

In your last two terms, squaring and cubing.

You seem to think that

(a-b)^n = a^n-b^n

. Hopefully, you know the correct expansions.

thanks man, i get it now

Reply 4

Dell PC 2

OP

17

Original post by davros

As an additional comment, I really wouldn't take out a factor of 2 as you're introducing fractions and the possibility of error in your working. I'm sure you're aware of the binomial expansion in its simplest form where you can do (a + b)^n = ???, and in particular here just take a = 2 and b = "the other bit".

I'll try that method out, but i always thought that you had to out a factor to get something like a(1+b/a)^n

I'm also kinda confused with this question
math 1.jpg

(edited 11 months ago)

Reply 5

old_engineer

11

Original post by Dell PC 2

I'll try that method out, but i always thought that you had to out a factor to get something like a(1+b/a)^n

I'm also kinda confused with this question

The power of x in the first term of this expansion is 5, while the power of x in the last term is -20. Somewhere in between is a term where the power of x is zero. This is what you're looking for.

Reply 6

davros

16

Original post by Dell PC 2

I'll try that method out, but i always thought that you had to out a factor to get something like a(1+b/a)^n

I'm also kinda confused with this question
math 1.jpg

You've got some advice on your new question, but surely you've seen things like:

(a + b)^2 = a^2 + 2ab + b^2

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

etc, just using Pascal's triangle directly?

This is how I first learned about binomial expansions - there's absolutely no requirement for the 1st term ['a'] to be 1. (Of course, when you come on to infinite series then it's slightly different because you want to manipulate the expression into a form where you can say something about convergence. But for a finite series there's no need to overcomplicate things :smile:

)

(edited 11 months ago)

Binomial question

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