Challenging Questions

Mathematics – Compulsory Part

Learning Unit: More about polynomials

Question M0-04-09

Given the expression \( x^6 – a^6 \):

1. Consider \( x^6 – a^6 = (x^2)^3 – (a^2)^3 \), factorize the expression.
2. Consider \( x^6 – a^6 = (x^3)^2 – (a^3)^2 \), factorize the expression.
3. Hence, find the H.C.F. and L.C.M. of \( x^3 + a^3 \), \( x^3 – a^3 \), and \( x^4 + a^2x^2 + a^4 \).

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