What is the factor form of ( x^2-64 )?
Answer and explanation
Correct answer: \((x+8)(x-8)\)
This expression is a difference of squares: \(x^2-64=x^2-8^2\). Using \(a^2-b^2=(a+b)(a-b)\), we get \((x+8)(x-8)\). In contrast, \((x-8)^2\) expands to \(x^2-16x+64\), so it is not correct. Exam tip: rewrite the constant term as a perfect square before applying the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\((x+8)(x-8)\)
Why is this the correct answer?
This expression is a difference of squares: \(x^2-64=x^2-8^2\). Using \(a^2-b^2=(a+b)(a-b)\), we get \((x+8)(x-8)\). In contrast, \((x-8)^2\) expands to \(x^2-16x+64\), so it is not correct. Exam tip: rewrite the constant term as a perfect square before applying 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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