What is the simplified form of \( (2x+3y)^2+(2x-3y)^2-(8x^2) \)?
Answer and explanation
Correct answer: 18y²
Use the identity \((a+b)^2+(a-b)^2=2a^2+2b^2\). Here, \(a=2x\) and \(b=3y\), so \((2x+3y)^2+(2x-3y)^2=2(2x)^2+2(3y)^2=8x^2+18y^2\). Subtracting \(8x^2\) gives \(18y^2\). The \(12xy\) and \(24xy\) options are incorrect because the mixed \(xy\) terms cancel when the two squares are added. Exam tip: When \((a+b)^2\) and \((a-b)^2\) occur together, look for cancellation of the mixed terms.
Frequently asked questions
What is the correct answer to this question?
18y²
Why is this the correct answer?
Use the identity \((a+b)^2+(a-b)^2=2a^2+2b^2\). Here, \(a=2x\) and \(b=3y\), so \((2x+3y)^2+(2x-3y)^2=2(2x)^2+2(3y)^2=8x^2+18y^2\). Subtracting \(8x^2\) gives \(18y^2\). The \(12xy\) and \(24xy\) options are incorrect because the mixed \(xy\) terms cancel when the two squares are added. Exam tip: When \((a+b)^2\) and \((a-b)^2\) occur together, look for cancellation of the mixed terms.
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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