Which of the following is equal to \\(x^2+18x+81\\)?
Answer and explanation
Correct answer: \((x+9)^2\)
Use the identity \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=9\), we get \((x+9)^2=x^2+2\cdot x\cdot9+9^2=x^2+18x+81\). Therefore, option A is correct. Option B would give the middle term \(-18x\), while option D omits the \(18x\) term. Exam tip: Take the square root of the constant term and use the sign of the middle term to choose between \((x+a)^2\) and \((x-a)^2\).
Frequently asked questions
What is the correct answer to this question?
\((x+9)^2\)
Why is this the correct answer?
Use the identity \((a+b)^2=a^2+2ab+b^2\). Taking \(a=x\) and \(b=9\), we get \((x+9)^2=x^2+2\cdot x\cdot9+9^2=x^2+18x+81\). Therefore, option A is correct. Option B would give the middle term \(-18x\), while option D omits the \(18x\) term. Exam tip: Take the square root of the constant term and use the sign of the middle term to choose between \((x+a)^2\) and \((x-a)^2\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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