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Which of the following expressions can be factorised as a perfect square using the identity \(a^2+2ab+b^2\)?
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Answer and explanation
Correct answer: \(x^2+10x+25\)
Taking \(a=x\) and \(b=5\) gives \(x^2+2(x)(5)+5^2=x^2+10x+25\). Hence it factorises as \((x+5)^2\). The expression \(x^2-10x+25\) has a negative middle term. Exam tip: always check the sign of the middle term.
Frequently asked questions
What is the correct answer to this question?
\(x^2+10x+25\)
Why is this the correct answer?
Taking \(a=x\) and \(b=5\) gives \(x^2+2(x)(5)+5^2=x^2+10x+25\). Hence it factorises as \((x+5)^2\). The expression \(x^2-10x+25\) has a negative middle term. Exam tip: always check the sign of the middle term.
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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