What is the simplified form of ( (2x-5)(2x+5)+25 )?
Answer and explanation
Correct answer: \(4x^2\)
Use the identity \((a-b)(a+b)=a^2-b^2\). Here, \(a=2x\) and \(b=5\), so \((2x-5)(2x+5)=4x^2-25\). Adding \(25\) gives \(4x^2-25+25=4x^2\). The option \(4x^2+25\) incorrectly fails to cancel the \(-25\) with the outside \(+25\). Exam tip: When conjugate factors appear, apply the difference-of-squares identity first.
Frequently asked questions
What is the correct answer to this question?
\(4x^2\)
Why is this the correct answer?
Use the identity \((a-b)(a+b)=a^2-b^2\). Here, \(a=2x\) and \(b=5\), so \((2x-5)(2x+5)=4x^2-25\). Adding \(25\) gives \(4x^2-25+25=4x^2\). The option \(4x^2+25\) incorrectly fails to cancel the \(-25\) with the outside \(+25\). Exam tip: When conjugate factors appear, apply the difference-of-squares identity first.
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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