Help! Urgemt Constant term of (x-(2/x^2))^9
is??
I expanded it and ended up with (1)^9 and (-2)^9.
Im stuck as to wat to do from here. should i add? or... what??
Term(r+1) C(9,r)(x^(9-r) * (-2/x^2)^r
= C(9,r) (-2)^r * x^(9-r)x^-2r)
= C(9,r) (-2)^r * x^(9 -3r)
to have a constant term there should be no x term, that is, 9-3r = 0
r = 3
So the constant term is
C(9,3)x^3 * (-2/x^2)^3
= 84(-8) = - 672
second last line should have been
C(9,3)x^6 * (-2/x^2)^3
thnx so much!
To find the constant term of the expression (x - (2/x^2))^9, you need to expand it using the binomial theorem.
The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a + b)^n can be written as the sum of terms of the form C(n, r) * a^(n-r) * b^r, where C(n, r) represents the binomial coefficient "n choose r".
In the case of (x - (2/x^2))^9, the constant term would be the term in which all the variable terms cancel out, leaving only constants.
To proceed, let's expand the expression:
(x - (2/x^2))^9 = C(9, 0) * x^9 * (-(2/x^2))^0 + C(9, 1) * x^8 * (-(2/x^2))^1 + C(9, 2) * x^7 * (-(2/x^2))^2 + ... + C(9, 8) * x * (-(2/x^2))^8 + C(9, 9) * (-(2/x^2))^9
Now, let's simplify each term. The constant term will be the term in which all the variable terms vanish.
For the first term, we have:
C(9, 0) * x^9 * (-(2/x^2))^0 = 1 * x^9 * 1 = x^9
In the last term, we have:
C(9, 9) * (-(2/x^2))^9 = 1 * (-(2/x^2))^9 = (-2)^9 / (x^2)^9 = 512 / x^18
So, the constant term is x^9.