What is the coefficient of x^2 in the expansion of (2x + 5)^4?
Practice Questions
Q1
What is the coefficient of x^2 in the expansion of (2x + 5)^4?
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Questions & Step-by-Step Solutions
What is the coefficient of x^2 in the expansion of (2x + 5)^4?
Step 1: Identify the expression we need to expand, which is (2x + 5)^4.
Step 2: Recall the binomial theorem, which states that (a + b)^n can be expanded using the formula: nCk * a^(n-k) * b^k, where nCk is the binomial coefficient.
Step 3: In our case, a = 2x, b = 5, and n = 4.
Step 4: We want the coefficient of x^2, which means we need to find the term where (2x) is raised to the power of 2.
Step 5: To find this term, we set k = 2 (since we want (2x)^2) and n-k = 4-2 = 2 (which means 5 is raised to the power of 2).
Step 6: Calculate the binomial coefficient 4C2, which is the number of ways to choose 2 items from 4. This is calculated as 4! / (2! * (4-2)!) = 6.
