What is the factorised form of \(x^2+14x+49\)?
Answer and explanation
Correct answer: \((x+7)^2\)
This expression is a perfect-square trinomial: \(a^2+2ab+b^2=(a+b)^2\). Here, \(a=x\) and \(b=7\), so \(2ab=2\cdot x\cdot7=14x\) and \(b^2=49\). Hence, \(x^2+14x+49=(x+7)^2\). Expanding \((x-7)^2\) gives the middle term \(-14x\), so it is incorrect. Exam tip: take the square roots of the first and last terms and check whether the middle term is \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\((x+7)^2\)
Why is this the correct answer?
This expression is a perfect-square trinomial: \(a^2+2ab+b^2=(a+b)^2\). Here, \(a=x\) and \(b=7\), so \(2ab=2\cdot x\cdot7=14x\) and \(b^2=49\). Hence, \(x^2+14x+49=(x+7)^2\). Expanding \((x-7)^2\) gives the middle term \(-14x\), so it is incorrect. Exam tip: take the square roots of the first and last terms and check whether the middle term is \(2ab\).
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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