Simplify ( (x-3)(x+3)+9 ).
Answer and explanation
Correct answer: \(x^2\)
Use the identity \((a-b)(a+b)=a^2-b^2\). Here, \((x-3)(x+3)=x^2-3^2=x^2-9\). Therefore, \((x^2-9)+9=x^2\), so option A is correct. \(x^2-9\) is only the product and does not include the outside \(+9\). Exam tip: when you see conjugate binomials \((a-b)(a+b)\), apply the difference-of-squares identity directly.
Frequently asked questions
What is the correct answer to this question?
\(x^2\)
Why is this the correct answer?
Use the identity \((a-b)(a+b)=a^2-b^2\). Here, \((x-3)(x+3)=x^2-3^2=x^2-9\). Therefore, \((x^2-9)+9=x^2\), so option A is correct. \(x^2-9\) is only the product and does not include the outside \(+9\). Exam tip: when you see conjugate binomials \((a-b)(a+b)\), apply the difference-of-squares identity directly.
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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