If that looks daunting, go back to the case of \((x+y)^3 = (x+y)(x+y)(x+y)\text{.}\) Why do we only have one \(x^3\) and \(y^3\) but three \(x^2y\) and \(xy^2\) terms? Every time we distribute over an \((x+y)\) we create two copies of what is left, one multiplied by \(x\text{,}\) the other multiplied by \(y\text{.}\) To get \(x^3\text{,}\) we need to pick the “multiplied by \(x\)” side every time (we don't have any \(y\)'s in the term). This will only happen once. On the other hand, to get \(x^2y\) we need to select the \(x\) side twice and the \(y\) side once. In other words, we need to pick one of the three \((x+y)\) terms to “contribute” their \(y\text{.}\)
in-context