Expand and simplify the algebraic binomial: (3x - 2y)².
Answer and explanation
Correct answer: C. 9x² - 12xy + 4y²
- Step 1: Apply expansion rule: (a - b)² = a² - 2ab + b². Step 2. a = 3x, b = 2y. Step 3. a² = (3x)² = 9x²; -2ab = -2(3x)(2y) = -12xy; b² = (2y)² = 4y². Step 4. Combine: 9x² - 12xy + 4y². Answer: 9x² - 12xy + 4y². Why not the others: 9x² - 6xy + 4y² forgets the factor of 2 in 2ab; 9x² + 12xy + 4y² uses positive middle sign; 9x² - 4y² omits the middle term.
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