Which of the following trinomials is a perfect square and can therefore be factorised as the square of a binomial?
Answer and explanation
Correct answer: \(x^2 - 12xy + 36y^2\)
A perfect-square trinomial has the form \(a^2-2ab+b^2=(a-b)^2\). In option A, \(x^2=(x)^2\), \(36y^2=(6y)^2\), and the middle term is \(-2\cdot x\cdot 6y=-12xy\). Thus, \(x^2-12xy+36y^2=(x-6y)^2\). In option D, the final term is \((6y)^2\), but its middle term should be \(-12xy\), not \(-6xy\). Exam tip: take the square roots of the first and last terms, then check whether the middle term is \(\pm2ab\).
Frequently asked questions
What is the correct answer to this question?
\(x^2 - 12xy + 36y^2\)
Why is this the correct answer?
A perfect-square trinomial has the form \(a^2-2ab+b^2=(a-b)^2\). In option A, \(x^2=(x)^2\), \(36y^2=(6y)^2\), and the middle term is \(-2\cdot x\cdot 6y=-12xy\). Thus, \(x^2-12xy+36y^2=(x-6y)^2\). In option D, the final term is \((6y)^2\), but its middle term should be \(-12xy\), not \(-6xy\). Exam tip: take the square roots of the first and last terms, then check whether the middle term is \(\pm2ab\).
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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