What is the value of \( (x+3)^2+(x+4)^2-2(x+3)(x+4) \)?
Answer and explanation
Correct answer: 1
The expression matches the identity \(a^2+b^2-2ab=(a-b)^2\), where \(a=x+3\) and \(b=x+4\). Therefore, its value is \(\big((x+3)-(x+4)\big)^2=(-1)^2=1\). It would be 0 only if the two terms were equal; here they differ by 1. Exam tip: First identify \(a^2+b^2-2ab\) and rewrite it as \((a-b)^2\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The expression matches the identity \(a^2+b^2-2ab=(a-b)^2\), where \(a=x+3\) and \(b=x+4\). Therefore, its value is \(\big((x+3)-(x+4)\big)^2=(-1)^2=1\). It would be 0 only if the two terms were equal; here they differ by 1. Exam tip: First identify \(a^2+b^2-2ab\) and rewrite it as \((a-b)^2\).
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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