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Which of the following quadratic expressions has factors that are two binomials with the same coefficient of x and opposite constant terms?

Answer and explanation

Correct answer: \(x^2-81\)

In \((x+p)(x-p)=x^2-p^2\), the middle terms cancel. Hence \(x^2-81=x^2-9^2=(x+9)(x-9)\). \(x^2+18x+81\) is a perfect square, not a product of conjugate binomials. Exam tip: opposite constants give a zero middle term.

Related tags

Algebraic IdentitiesQuadratic ExpressionsDifference Of SquaresConjugate BinomialsFactorisationClass 9 MathematicsExploring Algebraic IdentitiesMathematics

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