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Which of the following is the correct factorization of a² - b²?

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Question: Which of the following is the correct factorization of a² - b²?

Options:

  1. (a + b)(a - b)
  2. (a - b)(a - b)
  3. (a + b)(a + b)
  4. a² - 2ab + b²

Correct Answer: (a + b)(a - b)

Solution: 

a² - b² = (a + b)(a - b) by the difference of squares identity.

Which of the following is the correct factorization of a² - b²?

Practice Questions

Q1
Which of the following is the correct factorization of a² - b²?
  1. (a + b)(a - b)
  2. (a - b)(a - b)
  3. (a + b)(a + b)
  4. a² - 2ab + b²

Questions & Step-by-Step Solutions

Which of the following is the correct factorization of a² - b²?
  • Step 1: Identify the expression you want to factor, which is a² - b².
  • Step 2: Recognize that a² - b² is a special type of expression called a 'difference of squares'.
  • Step 3: Recall the formula for factoring a difference of squares, which is a² - b² = (a + b)(a - b).
  • Step 4: Apply the formula to your expression: a² - b² becomes (a + b)(a - b).
  • Step 5: Write down the final factored form: (a + b)(a - b).
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