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Which of the following expressions is a perfect-square trinomial and can be factorised using the identity \(a^2+2ab+b^2=(a+b)^2\)?
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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 \(10x=2\times x\times5\). Hence it has the form \((x+5)^2\). Option B has constant term 20, so it does not fit the identity. Exam tip: compare the middle term with \(2ab\).
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 \(10x=2\times x\times5\). Hence it has the form \((x+5)^2\). Option B has constant term 20, so it does not fit the identity. Exam tip: compare the middle term with \(2ab\).
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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