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What is the expansion of (2x - 3y)²?

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Question: What is the expansion of (2x - 3y)²?

Options:

  1. 4x² - 9y²
  2. 4x² - 12xy + 9y²
  3. 4x² + 9y²
  4. 4x² + 12xy + 9y²

Correct Answer: 4x² - 12xy + 9y²

Solution: 

(2x - 3y)² = 4x² - 12xy + 9y² by applying the square of a binomial.

What is the expansion of (2x - 3y)²?

Practice Questions

Q1
What is the expansion of (2x - 3y)²?
  1. 4x² - 9y²
  2. 4x² - 12xy + 9y²
  3. 4x² + 9y²
  4. 4x² + 12xy + 9y²

Questions & Step-by-Step Solutions

What is the expansion of (2x - 3y)²?
  • Step 1: Identify the expression to expand, which is (2x - 3y)².
  • Step 2: Recall the formula for the square of a binomial: (a - b)² = a² - 2ab + b².
  • Step 3: In our case, a = 2x and b = 3y.
  • Step 4: Calculate a²: (2x)² = 4x².
  • Step 5: Calculate b²: (3y)² = 9y².
  • Step 6: Calculate -2ab: -2 * (2x) * (3y) = -12xy.
  • Step 7: Combine all parts: 4x² - 12xy + 9y².
  • Step 8: Write the final expanded form: (2x - 3y)² = 4x² - 12xy + 9y².
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