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Which of the following expressions can be written as the product of a linear factor and a quadratic factor in the form \( (a-b)(a^2+ab+b^2) \)?
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Answer and explanation
Correct answer: \(a^3-b^3\)
The difference-of-cubes identity is \(a^3-b^3=(a-b)(a^2+ab+b^2)\). For \(a^3+b^3\), the first factor is \(a+b\). Exam tip: in the difference of cubes, the middle term of the quadratic factor is positive.
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What is the correct answer to this question?
\(a^3-b^3\)
Why is this the correct answer?
The difference-of-cubes identity is \(a^3-b^3=(a-b)(a^2+ab+b^2)\). For \(a^3+b^3\), the first factor is \(a+b\). Exam tip: in the difference of cubes, the middle term of the quadratic factor is positive.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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