( x^2+12x+36 ) is the perfect square of what?
Answer and explanation
Correct answer: \((x+6)^2\)
Use the identity \((a+b)^2=a^2+2ab+b^2\). Here, \(x^2+12x+36=x^2+2\cdot x\cdot6+6^2\), so it equals \((x+6)^2\). Note that \((x-6)^2=x^2-12x+36\), so it is not correct. Exam tip: use the sign of the middle term to decide whether the binomial has \(+\) or \(-\).
Frequently asked questions
What is the correct answer to this question?
\((x+6)^2\)
Why is this the correct answer?
Use the identity \((a+b)^2=a^2+2ab+b^2\). Here, \(x^2+12x+36=x^2+2\cdot x\cdot6+6^2\), so it equals \((x+6)^2\). Note that \((x-6)^2=x^2-12x+36\), so it is not correct. Exam tip: use the sign of the middle term to decide whether the binomial has \(+\) or \(-\).
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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