Independent Term in a Product of Binomials

Independent Term in a Product of Binomials

## Formula

For:

$$(ax^p+bx^q)^m(cx^r+dx^s)^n$$

the power of $$x$$ in the term obtained by choosing $$k$$ powers from the first binomial and $$l$$ powers from the second is:

$$p(m-k)+qk+r(n-l)+sl$$

For the independent term:

$$p(m-k)+qk+r(n-l)+sl=0$$

## Usage

- Used to determine whether a constant term exists in a product of binomial expansions.