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# Binomial expansion negative exponent help watch

1. Hi TSR, needed some help with this question:

(3-2x)^-1

I have to expand to get the coefficients of the x term and x^2 term, and to also state the range of x for which it is valid

Am I right to begin by taking (3-2x)^1 as 3(1-(2/3)x)^-1 so I can apply the binomial negative exponent formula?

edit: using this method I got 3+2x+(4/3)x^2, is this correct?
2. Bump
3. Another bump cus im desperate for please somebody
4. bump
5. (Original post by eternaforest)
Hi TSR, needed some help with this question:

(3-2x)^-1

I have to expand to get the coefficients of the x term and x^2 term, and to also state the range of x for which it is valid

Am I right to begin by taking (3-2x)^1 as 3(1-(2/3)x)^-1 so I can apply the binomial negative exponent formula?

edit: using this method I got 3+2x+(4/3)x^2, is this correct?
The 3 at the front should also be to the power of -1, i.e. it should be 1/3.
6. (Original post by tiny hobbit)
The 3 at the front should also be to the power of -1, i.e. it should be 1/3.
Ahh thank you, silly me

I will try it again
7. (Original post by eternaforest)
Hi TSR, needed some help with this question:

(3-2x)^-1

I have to expand to get the coefficients of the x term and x^2 term, and to also state the range of x for which it is valid

Am I right to begin by taking (3-2x)^1 as 3(1-(2/3)x)^-1 so I can apply the binomial negative exponent formula?

edit: using this method I got 3+2x+(4/3)x^2, is this correct?
If I'm reading you correctly, it looks like you've taken out the factor of 3 incorrectly.

Can you take it from here?
8. (Original post by Gregorius)
If I'm reading you correctly, it looks like you've taken out the factor of 3 incorrectly.

Can you take it from here?
yeah someone pointed out before, also I have to do the binomial expansion like (1+x)^a = 1 + ax + a(a-1)x^2/2! + a(a-1)(a-2)x^3/3! ...

I get 1/3 + 2/9x + 4/9x^2, is this right?
9. (Original post by eternaforest)
I get 1/3 + 2/9x + 4/9x^2, is this right?
Not quite - the term for isn't correct. Remember that

then set and remember to divide by that three!

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