In the expansion of (a + b)^6, which term will contain a^2b^4?
Practice Questions
1 question
Q1
In the expansion of (a + b)^6, which term will contain a^2b^4?
The 3rd term
The 4th term
The 5th term
The 6th term
The term containing a^2b^4 corresponds to C(6,2) * a^2 * b^4, which is the 4th term in the expansion.
Questions & Step-by-step Solutions
1 item
Q
Q: In the expansion of (a + b)^6, which term will contain a^2b^4?
Solution: The term containing a^2b^4 corresponds to C(6,2) * a^2 * b^4, which is the 4th term in the expansion.
Steps: 8
Step 1: Understand that (a + b)^6 means we are expanding the expression (a + b) multiplied by itself 6 times.
Step 2: Identify the general term in the expansion of (a + b)^n, which is given by the formula T(k) = C(n, k) * a^(n-k) * b^k, where C(n, k) is the binomial coefficient.
Step 3: In our case, n = 6. We want to find the term that contains a^2b^4. This means we need to set n-k = 2 (for a^2) and k = 4 (for b^4).
Step 4: From n-k = 2, we can find k: 6 - k = 2, so k = 4. This matches our requirement for b^4.
Step 5: Now, we need to calculate the binomial coefficient C(6, 4). This is the same as C(6, 2) because C(n, k) = C(n, n-k).
Step 7: The term containing a^2b^4 is therefore 15 * a^2 * b^4.
Step 8: Since we are looking for the position of this term in the expansion, we note that the terms are ordered by increasing powers of b. The term a^2b^4 is the 4th term.
