When (9x2 – 6xy + y2)5 is expanded and written in polynomial form with integral coefficients in descending order. The sum of the coefficients is ____?
The sum of the coefficients of any polynomial can be determined by
substituting 1 for all the variables. The thing to realize here is
if you substituted 1 for x when the expression is expanded and written
in polynomial form with integral coefficients in descending order, you
would get the same answer as you would if you substituted 1 in it when
it is not expanded and written that way. So we just substitute 1 in the
original as it is, and we will get the same answer as if we had expanded
it and written it in polynomial form with integral coefficients in
descending order, and substituted 1 in that:
(9x2 – 6xy + y2)5
(9·1² - 6·1·1 + 1²)5
(9 - 6 + 1)5
45
1024.
And that's what we'd get if we first expanded it and wrote it in polynomial
form with integral coefficients in descending order before we substituted
1 in it. The answer is c.
Edwin