What is the simplified form of (2a - 3[4a - 2(a - 5)])?
Answer and explanation
Correct answer: -4a - 30
The governing concept is the distributive law and careful handling of nested brackets. First simplify the innermost expression: 2(a - 5) = 2a - 10. Therefore, 4a - 2(a - 5) = 4a - (2a - 10) = 2a + 10. Now substitute this result into the full expression: 2a - 3(2a + 10). Distribute -3 across both terms: -3(2a + 10) = -6a - 30. Hence, 2a - 6a - 30 = -4a - 30. Therefore, option A is correct. Option B results from changing the sign of the constant incorrectly; options C and D fail to apply the negative multiplier to the variable term.
Frequently asked questions
What is the correct answer to this question?
-4a - 30
Why is this the correct answer?
The governing concept is the distributive law and careful handling of nested brackets. First simplify the innermost expression: 2(a - 5) = 2a - 10. Therefore, 4a - 2(a - 5) = 4a - (2a - 10) = 2a + 10. Now substitute this result into the full expression: 2a - 3(2a + 10). Distribute -3 across both terms: -3(2a + 10) = -6a - 30. Hence, 2a - 6a - 30 = -4a - 30. Therefore, option A is correct. Option B results from changing the sign of the constant incorrectly; options C and D fail to apply the negative multiplier to the variable term.
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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