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What is the value of (x + 2)² - (x² + 4)?

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Question: What is the value of (x + 2)² - (x² + 4)?

Options:

  1. 0
  2. 4
  3. 2x
  4. x² + 2

Correct Answer: 2x

Solution: 

(x + 2)² = x² + 4x + 4; thus, (x + 2)² - (x² + 4) = 4x.

What is the value of (x + 2)² - (x² + 4)?

Practice Questions

Q1
What is the value of (x + 2)² - (x² + 4)?
  1. 0
  2. 4
  3. 2x
  4. x² + 2

Questions & Step-by-Step Solutions

What is the value of (x + 2)² - (x² + 4)?
  • Step 1: Start with the expression (x + 2)² - (x² + 4).
  • Step 2: Expand (x + 2)². This means you multiply (x + 2) by itself: (x + 2)(x + 2).
  • Step 3: Use the distributive property (also known as FOIL) to expand: x*x + x*2 + 2*x + 2*2.
  • Step 4: Simplify the result from Step 3: x² + 2x + 2x + 4 = x² + 4x + 4.
  • Step 5: Now substitute this back into the original expression: (x² + 4x + 4) - (x² + 4).
  • Step 6: Distribute the negative sign to the second part: x² + 4x + 4 - x² - 4.
  • Step 7: Combine like terms: x² - x² + 4x + 4 - 4.
  • Step 8: The x² terms cancel out, and 4 - 4 equals 0, so you are left with 4x.
  • Step 9: Therefore, the final answer is 4x.
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