The binomial expansion formula also practices over exponents with negative values. Binomial Expression: A binomial expression is an algebraic expression that contains two dissimilar terms. So I did 1/ (3-2x)= (3-2x)^-1 and now not sure where to go = (3^-1) (1-2x/3)^-1 = (3^-1) (1+ (-1) (-2x/3)+ ( (-1) (-1-1) (-2x/3)^2)/2!) + n C n1 n 1 x y n - 1 + n C n n x 0 y n and it can be derived using mathematical induction. n = -2. Show that the quadratic approximation to $f(x)$ is given by $f(x)\approx3+\frac{13}{2}x+\frac{19}{4}x^2$. \(\left(\frac{n}{2}+1\right)\)th term is the middle term. Some of the binomial formulas for negative exponents are as follows: \((1+x)^{-1}=1-x+x^2-x^3+x^4-x^5+\cdots\), \((1-x)^{-1}=1+x+x^2+x^3+x^4+x^5+\cdots\), \((1+x)^{-3}=1-3x+6x^2-10x^3+15x^4+\cdots\), \((1-x)^{-3}=1+3x+6x^2+10x^3+15x^4+\cdots\). 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