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What is the result of (x + 1)² - (x - 1)²?

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Question: What is the result of (x + 1)² - (x - 1)²?

Options:

  1. 4x
  2. 4
  3. 0
  4. 2x

Correct Answer: 4

Solution: 

(x + 1)² - (x - 1)² = [(x² + 2x + 1) - (x² - 2x + 1)] = 4x.

What is the result of (x + 1)² - (x - 1)²?

Practice Questions

Q1
What is the result of (x + 1)² - (x - 1)²?
  1. 4x
  2. 4
  3. 0
  4. 2x

Questions & Step-by-Step Solutions

What is the result of (x + 1)² - (x - 1)²?
  • Step 1: Start with the expression (x + 1)² - (x - 1)².
  • Step 2: Expand (x + 1)² using the formula (a + b)² = a² + 2ab + b². Here, a = x and b = 1.
  • Step 3: (x + 1)² = x² + 2x + 1.
  • Step 4: Expand (x - 1)² using the same formula. Here, a = x and b = -1.
  • Step 5: (x - 1)² = x² - 2x + 1.
  • Step 6: Now substitute the expanded forms back into the original expression: (x² + 2x + 1) - (x² - 2x + 1).
  • Step 7: Distribute the negative sign in front of (x² - 2x + 1): (x² + 2x + 1) - x² + 2x - 1.
  • Step 8: Combine like terms: x² - x² + 2x + 2x + 1 - 1.
  • Step 9: This simplifies to 4x.
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