What is the correct expansion of \((2x-3)^2\)?
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Answer and explanation
Correct answer: \(4x^2-12x+9\)
Using \((a-b)^2=a^2-2ab+b^2\), take \(a=2x\) and \(b=3\). Then \((2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9\). Hence, option B is correct. Option A has an incorrect coefficient of the middle term, while option D has the wrong sign. Exam tip: the middle term in \((a-b)^2\) is always \(-2ab\).
Frequently asked questions
What is the correct answer to this question?
\(4x^2-12x+9\)
Why is this the correct answer?
Using \((a-b)^2=a^2-2ab+b^2\), take \(a=2x\) and \(b=3\). Then \((2x-3)^2=(2x)^2-2(2x)(3)+3^2=4x^2-12x+9\). Hence, option B is correct. Option A has an incorrect coefficient of the middle term, while option D has the wrong sign. Exam tip: the middle term in \((a-b)^2\) is always \(-2ab\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Quadratic expressions.
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