## Binomial Theorem

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

### Binomial Theorem

IB mathematics SL - Binomial Theorem

How can we find the constant term of the expansion of $(x-\frac{3}{x})^4$?

Thanks!
Brynlee

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

### Re: Binomial Theorem

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

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

In your question the general term is

${4}_C_{r} \ (x)^{4-r}(-\frac{3}{x})^r=$

${4}_C_{r} \ (x)^{4-r} ((-3)^r)(x^{-r})=$

${4}_C_{r} \ ((-3)^r)x^{4-r}(x^{-r})=$

${4}_C_{r} \ ((-3)^r)x^{4-2r}$ (1)

The constant term must be $x^0$

So, $4-2r=0 \Rightarrow r=2$

Then we can easily calculate the coefficient of this term by plugging in $r=2$ into equation (1)

${4}_C_{2} \ ((-3)^2)x^{4-2(2)}=$

$(6) (9)=54$

Hope these help!!
miranda

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