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Which of the following trinomials is a perfect-square trinomial and can therefore be factorised as the square of the same binomial?
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Answer and explanation
Correct answer: \(x^2-10x+25\)
In \(x^2-10x+25\), \(25=(-5)^2\) and the middle term is \(2\times x\times(-5)=-10x\). Hence it is \((x-5)^2\). \(x^2-25\) is a difference of squares, not a perfect-square trinomial. Exam tip: verify the middle term using \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\(x^2-10x+25\)
Why is this the correct answer?
In \(x^2-10x+25\), \(25=(-5)^2\) and the middle term is \(2\times x\times(-5)=-10x\). Hence it is \((x-5)^2\). \(x^2-25\) is a difference of squares, not a perfect-square trinomial. Exam tip: verify the middle term using \(2ab\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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