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

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

Options:

  1. x² + 3x + 2
  2. x² + 3x - 2
  3. 2x² + 2
  4. 2x² + 3x

Correct Answer: 2x² + 2

Solution: 

(x + 1)((x + 2) + (x - 2)) = (x + 1)(2x) = 2x² + 2x.

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

Practice Questions

Q1
What is the value of (x + 1)(x + 2) + (x + 1)(x - 2)?
  1. x² + 3x + 2
  2. x² + 3x - 2
  3. 2x² + 2
  4. 2x² + 3x

Questions & Step-by-Step Solutions

What is the value of (x + 1)(x + 2) + (x + 1)(x - 2)?
  • Step 1: Start with the expression (x + 1)(x + 2) + (x + 1)(x - 2).
  • Step 2: Notice that (x + 1) is common in both parts of the expression.
  • Step 3: Factor out (x + 1) from the expression: (x + 1)((x + 2) + (x - 2)).
  • Step 4: Simplify the expression inside the parentheses: (x + 2) + (x - 2) = x + 2 + x - 2 = 2x.
  • Step 5: Now the expression is (x + 1)(2x).
  • Step 6: Distribute (x + 1) with 2x: (x + 1)(2x) = 2x * x + 2x * 1 = 2x² + 2x.
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