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What is the coefficient of x^0 in the expansion of (3x - 4)^5?
What is the coefficient of x^0 in the expansion of (3x - 4)^5?
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Q1
What is the coefficient of x^0 in the expansion of (3x - 4)^5?
-1024
243
-243
1024
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The coefficient of x^0 is (-4)^5 = -1024.
Questions & Step-by-step Solutions
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Q
Q: What is the coefficient of x^0 in the expansion of (3x - 4)^5?
Solution:
The coefficient of x^0 is (-4)^5 = -1024.
Steps: 7
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Step 1: Understand that x^0 means we are looking for the constant term in the expansion.
Step 2: Use the Binomial Theorem, which states that (a + b)^n = sum of (n choose k) * a^(n-k) * b^k for k = 0 to n.
Step 3: In our case, a = 3x, b = -4, and n = 5.
Step 4: The constant term occurs when the power of x is 0, which happens when we choose all of b (-4) and none of a (3x).
Step 5: This means we need to calculate (-4)^5.
Step 6: Calculate (-4)^5 = -1024.
Step 7: Therefore, the coefficient of x^0 is -1024.
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