What are the factors of ( 4x^2-25 )?
Answer and explanation
Correct answer: \((2x+5)(2x-5)\)
The expression is a difference of squares: \(4x^2=(2x)^2\) and \(25=5^2\). Using \(a^2-b^2=(a+b)(a-b)\), with \(a=2x\) and \(b=5\), gives \((2x+5)(2x-5)\). On expansion, option B gives \(4x^2-15x-25\), so it is not correct. Exam tip: first check whether both terms are perfect squares separated by a minus sign.
Frequently asked questions
What is the correct answer to this question?
\((2x+5)(2x-5)\)
Why is this the correct answer?
The expression is a difference of squares: \(4x^2=(2x)^2\) and \(25=5^2\). Using \(a^2-b^2=(a+b)(a-b)\), with \(a=2x\) and \(b=5\), gives \((2x+5)(2x-5)\). On expansion, option B gives \(4x^2-15x-25\), so it is not correct. Exam tip: first check whether both terms are perfect squares separated by a minus sign.
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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