What is the simplified form of ( (2x+3y)^2+(2x-3y)^2 )?
Answer and explanation
Correct answer: \(8x^2+18y^2\)
Using \((a+b)^2+(a-b)^2=2a^2+2b^2\), take \(a=2x\) and \(b=3y\). This gives \(2(2x)^2+2(3y)^2=8x^2+18y^2\). The \(24xy\) terms cancel when the two squares are added, so option C is not correct. Exam tip: recognise the \((a+b)^2+(a-b)^2\) pattern and apply the identity directly.
Frequently asked questions
What is the correct answer to this question?
\(8x^2+18y^2\)
Why is this the correct answer?
Using \((a+b)^2+(a-b)^2=2a^2+2b^2\), take \(a=2x\) and \(b=3y\). This gives \(2(2x)^2+2(3y)^2=8x^2+18y^2\). The \(24xy\) terms cancel when the two squares are added, so option C is not correct. Exam tip: recognise the \((a+b)^2+(a-b)^2\) pattern and apply the identity 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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