Question

find the GCD of a3-1 and a2-1

Answer 1

By finding the  h c f we have

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

 a^2 - b^2 = (a + b)(a - b)

 a^3 - 1 = (a-1)(a^2 + a + 1)

   a^2 - 1 = (a + 1)(a - 1)

The common factor is (a - 1).

Answer 2

as we know formulas

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

a^2 - b^2 = (a + b)(a - b)

taking a^3-1 instead of a^3 -b^3

replacing b by 1

in both of above equations

 a^3 - 1 = (a-1)(a^2 + a + 1)

 a^2 - 1 = (a + 1)(a - 1)

we can clearly see that  The common factor is (a - 1)