Notice the following patterns:
(m -a)(m-b) = [m^2 - ma - mb + (ab)] = [ m^2 - (a+b)m + (ab)]
[ m^2 - (a+b)m + (ab)] [m - c ] =
m^3 - (a+b)m^2 + (ab)m - cm^2 + (ac)m + (bc)m - abc =
m^3 - (a + b + c)m^2 + (ab + ac + bc)m - abc
Let (a,b,c,d,e.......z) be denoted as SetZ.....so we have.....
(m-a)(m-b)(m-c)......(m-z) =
m^26 - (sum of all elements in SetZ taken one at a time)m^25 + (sum of all elements in SetZ taken two at a time)m^24 - (sum of all elements of SetZ taken three at a time)m^23 +.........+ (sum of all elements in SetZ taken 24 at a time)m^2 -(sum of all elements of SetZ taken 25 at a time)m + (the product of all elements in SetZ)
I believe this is correct......!!! {Can someone else - Melody, Alan?? - check my logic}
