What is the simplified form of \( (x+a)(x-a)(x^2+a^2) \)?
Answer and explanation
Correct answer: \(x^4-a^4\)
First use the identity \((x+a)(x-a)=x^2-a^2\). The expression becomes \((x^2-a^2)(x^2+a^2)\). Applying \((p-q)(p+q)=p^2-q^2\), with \(p=x^2\) and \(q=a^2\), gives \(x^4-a^4\). Option D is the expansion of \((x^2-a^2)^2\), so it is not applicable here. Exam tip: identify conjugate factors step by step and use the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
\(x^4-a^4\)
Why is this the correct answer?
First use the identity \((x+a)(x-a)=x^2-a^2\). The expression becomes \((x^2-a^2)(x^2+a^2)\). Applying \((p-q)(p+q)=p^2-q^2\), with \(p=x^2\) and \(q=a^2\), gives \(x^4-a^4\). Option D is the expansion of \((x^2-a^2)^2\), so it is not applicable here. Exam tip: identify conjugate factors step by step and 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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