What is the simplified form of \( (3a+2b)^2-(3a-2b)^2 \)?
Answer and explanation
Correct answer: \(24ab\)
Use the identity \((x+y)^2-(x-y)^2=4xy\). Here, \(x=3a\) and \(y=2b\), so the expression equals \(4\times 3a\times 2b=24ab\). Hence, option B is correct. \(9a^2-4b^2\) is the product \((3a+2b)(3a-2b)\), whereas the question gives the difference of the squares of these two binomials. Exam tip: for an expression of the form \((x+y)^2-(x-y)^2\), apply \(4xy\) directly.
Frequently asked questions
What is the correct answer to this question?
\(24ab\)
Why is this the correct answer?
Use the identity \((x+y)^2-(x-y)^2=4xy\). Here, \(x=3a\) and \(y=2b\), so the expression equals \(4\times 3a\times 2b=24ab\). Hence, option B is correct. \(9a^2-4b^2\) is the product \((3a+2b)(3a-2b)\), whereas the question gives the difference of the squares of these two binomials. Exam tip: for an expression of the form \((x+y)^2-(x-y)^2\), apply \(4xy\) directly.
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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