Answer: 20
Explanation:
To find the coefficient of the term in the expansion of (a - b^2)^6 that contains a^3b^6, you can use the binomial theorem or Pascal's triangle.
The binomial theorem states that the expansion of (a - b^2)^n is given by:
(a - b^2)^n = C(n, 0)a^n(-b^2)^0 + C(n, 1)a^(n-1)(-b^2)^1 + C(n, 2)a^(n-2)(-b^2)^2 + ... + C(n, k)a^(n-k)(-b^2)^k + ... + C(n, n)a^0(-b^2)^n
Where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).
In your case, you're interested in the term containing a^3b^6, so k = 3 and n = 6:
C(6, 3)a^(6-3)(-b^2)^3 = C(6, 3)a^3(-b^6)
Now, calculate the binomial coefficient C(6, 3):
C(6, 3) = 6! / (3!(6-3)!) = (6*5*4) / (3*2*1) = 20
So, the coefficient of the term in (a - b^2)^6 that contains a^3b^6 is 20.