01 What is obtained after simplifying 3a² − 2ab + 5b² − (2a² + ab − 4b²)?
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Answer and explanation
Correct answer: C. a² − 3ab + 9b²
Explanation: The governing concept is subtracting a grouped algebraic expression and then combining like terms. The minus sign before the bracket changes every sign inside it: 3a² − 2ab + 5b² − (2a² + ab − 4b²) becomes 3a² − 2ab + 5b² − 2a² − ab + 4b². Collect the a² terms to get 3a² − 2a² = a². Collect the ab terms to get −2ab − ab = −3ab. Finally, collect the b² terms: 5b² + 4b² = 9b². The result is a² − 3ab + 9b², so option C is correct. Option A loses one ab contribution, option B mishandles the a² terms, and option D gives the wrong coefficient of ab.