What is the expansion of \((3x+2)^2\)?
Answer and explanation
Correct answer: \(9x^2+12x+4\)
Use the identity \((a+b)^2=a^2+2ab+b^2\). With \(a=3x\) and \(b=2\), we get \((3x)^2+2(3x)(2)+2^2=9x^2+12x+4\). Therefore, option A is correct. Option B incorrectly uses only \(ab\) instead of the middle term \(2ab\). Exam tip: in \((a+b)^2\), the middle term is always \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\(9x^2+12x+4\)
Why is this the correct answer?
Use the identity \((a+b)^2=a^2+2ab+b^2\). With \(a=3x\) and \(b=2\), we get \((3x)^2+2(3x)(2)+2^2=9x^2+12x+4\). Therefore, option A is correct. Option B incorrectly uses only \(ab\) instead of the middle term \(2ab\). Exam tip: in \((a+b)^2\), the middle term is always \(2ab\).
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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