What is the value of ( (5m+4n)(5m-4n) )?
Answer and explanation
Correct answer: \(25m^2-16n^2\)
This uses the identity \((a+b)(a-b)=a^2-b^2\). Here, \(a=5m\) and \(b=4n\), so \((5m+4n)(5m-4n)=(5m)^2-(4n)^2=25m^2-16n^2\). Option D resembles the expansion of \((5m-4n)^2\), but the given factors have opposite signs. Exam tip: in conjugate factors, the middle terms cancel out.
Frequently asked questions
What is the correct answer to this question?
\(25m^2-16n^2\)
Why is this the correct answer?
This uses the identity \((a+b)(a-b)=a^2-b^2\). Here, \(a=5m\) and \(b=4n\), so \((5m+4n)(5m-4n)=(5m)^2-(4n)^2=25m^2-16n^2\). Option D resembles the expansion of \((5m-4n)^2\), but the given factors have opposite signs. Exam tip: in conjugate factors, the middle terms cancel out.
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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