What do we get after simplifying ( (p+9)(p-9) )?
Answer and explanation
Correct answer: \(p^2-81\)
This expression uses the identity \((a+b)(a-b)=a^2-b^2\). Taking \(a=p\) and \(b=9\), we get \((p+9)(p-9)=p^2-9^2=p^2-81\). \(p^2+81\) is a sum of squares, so it does not result from this product. Exam tip: when two binomials have the same terms with opposite signs, use the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\(p^2-81\)
Why is this the correct answer?
This expression uses the identity \((a+b)(a-b)=a^2-b^2\). Taking \(a=p\) and \(b=9\), we get \((p+9)(p-9)=p^2-9^2=p^2-81\). \(p^2+81\) is a sum of squares, so it does not result from this product. Exam tip: when two binomials have the same terms with opposite signs, use the difference-of-squares identity.
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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