Simplify ( (2x+3)^2-(4x^2+9) ).
Answer and explanation
Correct answer: \(12x\)
Using \((a+b)^2=a^2+2ab+b^2\), \((2x+3)^2=4x^2+12x+9\). Subtracting \(4x^2+9\) cancels the \(4x^2\) and \(9\) terms, leaving \(12x\). \(6x\) is a close distractor because the middle term is \(2\times 2x\times 3=12x\). Exam tip: always calculate the middle term of a binomial square as \(2ab\).
Frequently asked questions
What is the correct answer to this question?
\(12x\)
Why is this the correct answer?
Using \((a+b)^2=a^2+2ab+b^2\), \((2x+3)^2=4x^2+12x+9\). Subtracting \(4x^2+9\) cancels the \(4x^2\) and \(9\) terms, leaving \(12x\). \(6x\) is a close distractor because the middle term is \(2\times 2x\times 3=12x\). Exam tip: always calculate the middle term of a binomial square as \(2ab\).
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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