What is the simplified form of ( (3x+5)^2-(3x-1)^2 )?
Answer and explanation
Correct answer: 36x+24
Use the identity \(a^2-b^2=(a+b)(a-b)\). Here, \(a=3x+5\) and \(b=3x-1\). Thus, \(a+b=6x+4\) and \(a-b=6\). Therefore, \((6x+4)\times6=36x+24\). Option B results from an incorrect multiplication of the \(6x\) term by 6. Exam tip: identify the two squared expressions first and apply the identity directly instead of expanding both squares.
Frequently asked questions
What is the correct answer to this question?
36x+24
Why is this the correct answer?
Use the identity \(a^2-b^2=(a+b)(a-b)\). Here, \(a=3x+5\) and \(b=3x-1\). Thus, \(a+b=6x+4\) and \(a-b=6\). Therefore, \((6x+4)\times6=36x+24\). Option B results from an incorrect multiplication of the \(6x\) term by 6. Exam tip: identify the two squared expressions first and apply the identity directly instead of expanding both squares.
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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