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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

\( (a-b)(a^2+ab+b^2) \)?

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.

Related tags

Algebraic IdentitiesDifference Of CubesFactorisationPolynomialsClass 9 MathematicsExploring Algebraic IdentitiesMathematicsClass 9 Mcq

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