What is the 8th term of (3x-1/2y)^10
To find the 8th term of the expansion (3x - 1/2y)^10, you can use the binomial theorem. The binomial theorem states that the coefficient of the kth term in the expansion of a binomial (a + b)^n is given by the formula:
C(n, k) * a^(n-k) * b^k
Where C(n, k) represents the binomial coefficient, also known as choose function, which is the number of ways to choose k items from a set of n items.
In this case, the binomial is (3x - 1/2y) with n = 10. We want to find the 8th term, which means k = 8.
Let's calculate the 8th term step-by-step:
Step 1: Calculate the binomial coefficient using the formula C(n, k) = n! / (k! * (n-k)!). In this case, we have C(10, 8) = 10! / (8! * (10-8)!) = 45.
Step 2: Calculate the powers of each term. In our binomial (3x - 1/2y), we have (3x)^(10-8) * (-1/2y)^8.
Simplifying these terms:
- (3x)^(10-8) = (3x)^2 = 9x^2
- (-1/2y)^8 = (-1)^8 * (1/2)^8 * y^8 = 1 * 1/256 * y^8 = y^8/256.
Step 3: Multiply these terms together:
8th term = 45 * 9x^2 * y^8/256
Simplifying further:
8th term = (45 * 9 * x^2 * y^8) / 256
Therefore, the 8th term of the expansion (3x - 1/2y)^10 is (45 * 9 * x^2 * y^8) / 256.