Which of the following expressions is a perfect-square trinomial and can therefore be factorised as the product of two identical binomials?
Answer and explanation
Correct answer: \(16x^2-40xy+25y^2\)
In option A, \(16x^2=(4x)^2\) and \(25y^2=(5y)^2\). Its middle term is \(-40xy=-2(4x)(5y)\), so \(16x^2-40xy+25y^2=(4x-5y)^2\). In option B, the last term is \(20y^2\), but \(25y^2\) is required for a perfect-square trinomial with this middle term. Exam tip: take the square roots of the first and last terms, then check whether the middle term equals \(\pm2ab\).
Frequently asked questions
What is the correct answer to this question?
\(16x^2-40xy+25y^2\)
Why is this the correct answer?
In option A, \(16x^2=(4x)^2\) and \(25y^2=(5y)^2\). Its middle term is \(-40xy=-2(4x)(5y)\), so \(16x^2-40xy+25y^2=(4x-5y)^2\). In option B, the last term is \(20y^2\), but \(25y^2\) is required for a perfect-square trinomial with this middle term. Exam tip: take the square roots of the first and last terms, then check whether the middle term equals \(\pm2ab\).
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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