Question

List all collected terms with coefficient 13 in the expansion of (c + a + m + e + r + a)13. Explain how you determined the list. 

Answer 1

Let X=a+m+e+r+a. (c+X)^13=c^13+13c^12*X+...+13cX^12+X^13.

So there are two terms in the expansion with coefficient 13: 13Xc^12 and 13cX^12.

The expansion of X^12 will have no terms with coefficient 13 so we have to look at 13Xc^12 and 13cX^12 more closely substituting back for X: 13c^12(a+m+e+r+a) and 13c(a+m+e+r+a)^12.

So we have 13ac^12+13mc^12+13ec^12+13rc^12+13ac^12 and 13ca^12+13cm^12+13ce^12+13cr^12+13ca^12. All other terms have different coefficients.