## Binomial Theorem ib maths sl

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

### Binomial Theorem ib maths sl

IB math SL - Binomial Theorem

How can we find the coefficient of the term $x^2$ of the expansion of $(x-\frac{1}{x})^8$?

Thanks!
Brynlee

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm

### Re: Binomial Theorem ib maths sl

$(x-\frac{1}{x})^8$

The general term of a binomial expansion of the form $(a+b)^n$ is given by the following formula:

${n}_C_{r} \ a^{n-r}b^r$

Concerning this question the general term is :

${8}_C_{r} \ (x)^{8-r}(-\frac{1}{x})^r=$

${8}_C_{r} \ (x)^{8-r} ((-1)^r)(x^{-r})=$

${8}_C_{r} \ ((-1)^r)x^{8-r}(x^{-r})=$

${8}_C_{r} \ ((-1)^r)x^{8-2r}$ (1)

The term that must be examined is $x^2$.

So, $8-2r=2 \Rightarrow r=3$

Then we can easily calculate the coefficient of this term by plugging in $r=3$ into equation (1).

${8}_C_{3}\ (-1^3)x^{8-2(3)}=$

$(56)(-1)x^{2}= -56x^{2}$

Hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: Binomial Theorem ib maths sl

Thanks miranda!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm