What is the simplified form of \( (2x+3)^2-(2x+1)^2 \)?
Answer and explanation
Correct answer: \(8x+8\)
This is a difference of squares: \(a^2-b^2=(a+b)(a-b)\). Here, \(a=2x+3\) and \(b=2x+1\). Thus, \(a+b=4x+4\) and \(a-b=2\), so the expression becomes \((4x+4)\times2=8x+8\). The expression \(4x+4\) is only \(a+b\), not the final simplified form. Exam tip: first identify the two bases of the squares, then apply the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\(8x+8\)
Why is this the correct answer?
This is a difference of squares: \(a^2-b^2=(a+b)(a-b)\). Here, \(a=2x+3\) and \(b=2x+1\). Thus, \(a+b=4x+4\) and \(a-b=2\), so the expression becomes \((4x+4)\times2=8x+8\). The expression \(4x+4\) is only \(a+b\), not the final simplified form. Exam tip: first identify the two bases of the squares, then apply the difference-of-squares identity.
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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