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Find the value of (1 + x)^10 at x = 2.

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Question: Find the value of (1 + x)^10 at x = 2.

Options:

  1. 1024
  2. 2048
  3. 512
  4. 256

Correct Answer: 2048

Solution: 

Using the binomial theorem, (1 + 2)^10 = 3^10 = 59049.

Find the value of (1 + x)^10 at x = 2.

Practice Questions

Q1
Find the value of (1 + x)^10 at x = 2.
  1. 1024
  2. 2048
  3. 512
  4. 256

Questions & Step-by-Step Solutions

Find the value of (1 + x)^10 at x = 2.
  • Step 1: Identify the expression we need to evaluate, which is (1 + x)^10.
  • Step 2: Substitute the value of x with 2 in the expression. This gives us (1 + 2)^10.
  • Step 3: Simplify the expression inside the parentheses. 1 + 2 equals 3, so we have (3)^10.
  • Step 4: Calculate 3 raised to the power of 10. This means multiplying 3 by itself 10 times.
  • Step 5: The result of 3^10 is 59049.
  • Binomial Theorem – The binomial theorem provides a formula for expanding expressions of the form (a + b)^n, where n is a non-negative integer.
  • Substitution – The process of replacing a variable with a specific value to evaluate an expression.
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