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What is the value of (x + 1)^5 when x = 2?

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Question: What is the value of (x + 1)^5 when x = 2?

Options:

  1. 32
  2. 64
  3. 128
  4. 256

Correct Answer: 128

Solution: 

Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.

What is the value of (x + 1)^5 when x = 2?

Practice Questions

Q1
What is the value of (x + 1)^5 when x = 2?
  1. 32
  2. 64
  3. 128
  4. 256

Questions & Step-by-Step Solutions

What is the value of (x + 1)^5 when x = 2?
  • Step 1: Identify the expression we need to evaluate, which is (x + 1)^5.
  • Step 2: Substitute the value of x = 2 into the expression. This gives us (2 + 1)^5.
  • Step 3: Simplify (2 + 1) to get 3. Now we have 3^5.
  • Step 4: Calculate 3^5. This means multiplying 3 by itself 5 times: 3 * 3 * 3 * 3 * 3.
  • Step 5: First, calculate 3 * 3 = 9.
  • Step 6: Next, multiply 9 by 3 to get 27.
  • Step 7: Then, multiply 27 by 3 to get 81.
  • Step 8: Finally, multiply 81 by 3 to get 243.
  • Step 9: Therefore, the value of (x + 1)^5 when x = 2 is 243.
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