Independent Term

Independent Term

## Definition / Concept

An independent term is a term that does not contain the variable.

## Formula

For:

$$(ax^p+bx^q)^n$$

the $(r+1)$th term is:

$$T_{r+1}={}^nC_r a^{n-r}b^r x^{p(n-r)+qr}$$

For the term independent of $x$:

$$p(n-r)+qr=0$$

Therefore:

$$r=\frac{pn}{p-q}$$

provided the value of $$r$$ is an integer satisfying:

$$0\le r\le n$$

## Usage

- Used to find the term that contains no variable in a binomial expansion.