What is the simplified form of (2a - 3[4a - 2(a - 5)])?
Answer and explanation
Correct answer: -4a - 30
The governing concepts are the distributive law, the order of simplifying nested brackets, and careful handling of negative signs. First simplify the innermost part: 2(a − 5) = 2a − 10. Hence 4a − 2(a − 5) = 4a − (2a − 10) = 4a − 2a + 10 = 2a + 10. Substituting this result gives 2a − 3(2a + 10). Distributing −3 produces −6a − 30, so the complete expression becomes 2a − 6a − 30 = −4a − 30. Therefore option A is correct. Option B has the wrong constant sign, while C and D fail to distribute the negative multiplier correctly.
Frequently asked questions
What is the correct answer to this question?
-4a - 30
Why is this the correct answer?
The governing concepts are the distributive law, the order of simplifying nested brackets, and careful handling of negative signs. First simplify the innermost part: 2(a − 5) = 2a − 10. Hence 4a − 2(a − 5) = 4a − (2a − 10) = 4a − 2a + 10 = 2a + 10. Substituting this result gives 2a − 3(2a + 10). Distributing −3 produces −6a − 30, so the complete expression becomes 2a − 6a − 30 = −4a − 30. Therefore option A is correct. Option B has the wrong constant sign, while C and D fail to distribute the negative multiplier correctly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Algebraic expressions.
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