What is the 3rd term in the expansion of (a + b)^6?
Practice Questions
1 question
Q1
What is the 3rd term in the expansion of (a + b)^6?
15ab^5
20ab^5
30ab^5
6ab^5
The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the 3rd term in the expansion of (a + b)^6?
Solution: The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.
Steps: 8
Step 1: Identify the expression we are expanding, which is (a + b)^6.
Step 2: Understand that we need to find the 3rd term in the expansion.
Step 3: Use the binomial theorem, which states that the nth term in the expansion of (x + y)^n is given by nCk * x^(n-k) * y^k, where k is the term number minus 1.
Step 4: For (a + b)^6, n is 6. To find the 3rd term, we set k = 2 (since 3rd term means k = 2).
Step 5: Calculate 6C2, which is the number of combinations of 6 items taken 2 at a time. This is calculated as 6! / (2!(6-2)!) = 15.
Step 6: Now, substitute n, k, and the variables into the formula: 6C2 * a^(6-2) * b^2.
Step 7: This simplifies to 15 * a^4 * b^2.
Step 8: Therefore, the 3rd term in the expansion of (a + b)^6 is 15a^4b^2.
