Simplify ( (7m+3n)(7m-3n) ).
Answer and explanation
Correct answer: \(49m^2-9n^2\)
The expression uses the identity \((a+b)(a-b)=a^2-b^2\), with \(a=7m\) and \(b=3n\). Therefore, \((7m+3n)(7m-3n)=(7m)^2-(3n)^2=49m^2-9n^2\). Option D resembles the expansion of \((a-b)^2\), but this expression is a product of conjugate binomials. Exam tip: in \((a+b)(a-b)\), the middle terms always cancel.
Frequently asked questions
What is the correct answer to this question?
\(49m^2-9n^2\)
Why is this the correct answer?
The expression uses the identity \((a+b)(a-b)=a^2-b^2\), with \(a=7m\) and \(b=3n\). Therefore, \((7m+3n)(7m-3n)=(7m)^2-(3n)^2=49m^2-9n^2\). Option D resembles the expansion of \((a-b)^2\), but this expression is a product of conjugate binomials. Exam tip: in \((a+b)(a-b)\), the middle terms always cancel.
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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