$If p and q are positive real numbers, then the coefficients of x^p and x^q in the expansion of {\left(1+x\right)}^{p-q} will be$

$$\begin{gathered} The coefficient of x^p in {(1+x)}^{p+q} is C(p+q,p) and the coefficient of x^q in the \\ expansion of {(1+x)}^{p+q}is C(p+q,q) \\ Both coefficents are equal to \frac{\left(p+q\right)!}{p!q!} \end{gathered}$$