What is the simplified form of \( (x-1)(x+1)(x^2+1) \)?
Answer and explanation
Correct answer: \(x^4-1\)
First, use the identity \((x-1)(x+1)=x^2-1\). The expression then becomes \((x^2-1)(x^2+1)\), which again has the form \((a-b)(a+b)=a^2-b^2\). Therefore, it simplifies to \(x^4-1\). \(x^4+1\) is not the result of this difference-of-squares identity. Exam tip: identify conjugate binomial pairs and apply identities step by step.
Frequently asked questions
What is the correct answer to this question?
\(x^4-1\)
Why is this the correct answer?
First, use the identity \((x-1)(x+1)=x^2-1\). The expression then becomes \((x^2-1)(x^2+1)\), which again has the form \((a-b)(a+b)=a^2-b^2\). Therefore, it simplifies to \(x^4-1\). \(x^4+1\) is not the result of this difference-of-squares identity. Exam tip: identify conjugate binomial pairs and apply identities step by step.
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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