Which of the following trinomials is a perfect-square trinomial and can therefore be factorised as the square of a binomial?
Answer and explanation
Correct answer: \(x^2+10x+25\)
A perfect-square trinomial has the form \(a^2+2ab+b^2=(a+b)^2\). Here, \(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=(x+5)^2\), so option A is correct. In option B, the constant term \(20\) is not \(5^2\); in option C, the middle term should be \(2\cdot x\cdot5=10x\), not \(5x\). Exam tip: take the square roots of the first and last terms, then check whether the middle term is twice their product.
Frequently asked questions
What is the correct answer to this question?
\(x^2+10x+25\)
Why is this the correct answer?
A perfect-square trinomial has the form \(a^2+2ab+b^2=(a+b)^2\). Here, \(x^2+10x+25=x^2+2\cdot x\cdot5+5^2=(x+5)^2\), so option A is correct. In option B, the constant term \(20\) is not \(5^2\); in option C, the middle term should be \(2\cdot x\cdot5=10x\), not \(5x\). Exam tip: take the square roots of the first and last terms, then check whether the middle term is twice their product.
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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