Which is the correct factorised form of (x^2+2xy+y^2-25)?
Answer and explanation
Correct answer: \((x+y-5)(x+y+5)\)
In \(x^2+2xy+y^2-25\), the first three terms form \((x+y)^2\), and \(25=5^2\). Hence the expression is \((x+y)^2-5^2\). Using \(a^2-b^2=(a-b)(a+b)\), we get \((x+y-5)(x+y+5)\). Option B would involve \((x-y)^2\), whose middle term is \(-2xy\), so it is incorrect. Exam tip: first recognise expressions of the form \(x^2\pm2xy+y^2\) as perfect squares.
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What is the correct answer to this question?
\((x+y-5)(x+y+5)\)
Why is this the correct answer?
In \(x^2+2xy+y^2-25\), the first three terms form \((x+y)^2\), and \(25=5^2\). Hence the expression is \((x+y)^2-5^2\). Using \(a^2-b^2=(a-b)(a+b)\), we get \((x+y-5)(x+y+5)\). Option B would involve \((x-y)^2\), whose middle term is \(-2xy\), so it is incorrect. Exam tip: first recognise expressions of the form \(x^2\pm2xy+y^2\) as perfect squares.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Factorisation.
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