I uploaded a picture of what I am stuck on. I understand the equation of motion 3.4.5a for a damped oscillator but I don't understand how to use binomial theorem to get the expanded equation 3.4.5b. I am no where near clever enough to figure this one out. I know how to use binomial theorem to expand something with two terms but the fact that this has three terms and is only to the first power throws me off and I don't know how to apply the binomial theorem. If anyone could give me any hints, I would very much appreciate it. Thanks so much for reading!