What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2
Practice Questions
Q1
What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2020)
70
56
28
8
Questions & Step-by-Step Solutions
What is the value of the term containing x^4 in the expansion of (x + 1/2)^8? (2020)
Step 1: Identify the expression we are expanding, which is (x + 1/2)^8.
Step 2: Use the binomial theorem to find the general term in the expansion. The general term is given by C(n, k) * (a^k) * (b^(n-k)), where n is the exponent, k is the term number, a is the first term, and b is the second term.
Step 3: In our case, n = 8, a = x, and b = 1/2. We want the term that contains x^4, which means we need k = 4.
Step 4: Calculate C(8, 4), which is the number of combinations of 8 items taken 4 at a time. C(8, 4) = 8! / (4! * (8-4)!) = 70.
Step 5: Calculate (1/2)^4, which is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.
Step 6: Multiply the results from Step 4 and Step 5 to find the value of the term containing x^4: 70 * (1/16) = 70/16 = 4.375.
