Which of the following expressions is a perfect-square trinomial for all real values of the variables?
Answer and explanation
Correct answer: \(x^2+2xy+y^2\)
\(x^2+2xy+y^2=(x+y)^2\), so it is a perfect-square trinomial. Check the middle term: \(2xy=2\cdot x\cdot y\). In option B, the middle term is only \(xy\), so it cannot be \((x+y)^2\). Exam tip: compare the middle term with twice the product of the square roots of the end terms.
Frequently asked questions
What is the correct answer to this question?
\(x^2+2xy+y^2\)
Why is this the correct answer?
\(x^2+2xy+y^2=(x+y)^2\), so it is a perfect-square trinomial. Check the middle term: \(2xy=2\cdot x\cdot y\). In option B, the middle term is only \(xy\), so it cannot be \((x+y)^2\). Exam tip: compare the middle term with twice the product of the square roots of the end terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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