Binomial Expansion by Substitution

Binomial Expansion by Substitution

## Formula

If:

$$P(x)=(1+x)^n$$

then replacing $x$ by any expression $f(x)$ gives:

$$P(f(x))=(1+f(x))^n$$

and:

$$(1+f(x))^n=\sum_{r=0}^{n}{}^nC_r[f(x)]^r$$

## Usage

- Used when the binomial contains an algebraic expression instead of a single variable.