What is the simplified form of ( (x-y)^2-x^2-y^2 )?
Answer and explanation
Correct answer: \(-2xy\)
Using the identity \((x-y)^2=x^2-2xy+y^2\), the expression becomes \(x^2-2xy+y^2-x^2-y^2\). The \(x^2\) and \(y^2\) terms cancel, leaving \(-2xy\). The result \(2xy\) would arise from \((x+y)^2\), not \((x-y)^2\). Exam tip: the middle term in \((a-b)^2\) is always negative, \(-2ab\).
Frequently asked questions
What is the correct answer to this question?
\(-2xy\)
Why is this the correct answer?
Using the identity \((x-y)^2=x^2-2xy+y^2\), the expression becomes \(x^2-2xy+y^2-x^2-y^2\). The \(x^2\) and \(y^2\) terms cancel, leaving \(-2xy\). The result \(2xy\) would arise from \((x+y)^2\), not \((x-y)^2\). Exam tip: the middle term in \((a-b)^2\) is always negative, \(-2ab\).
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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