Let’s find G.C.D of the following algebraic expression:

x²-1, x²-2x + 1, x³ + x²-2x

Factors of x²-1=(x + 1)(x-1)

Factors of x²-2x + 1

x²-2x + 1=x²-x-x + 1

=x(x-1)-1(x-1)

=(x-1)²

=(x-1)×(x-1)

Factors of x³ + x²-2x

x³ + x²-2x=x(x² + x-2)

=x(x² + 2x-x-2)

=x[{x(x + 2)-1(x + 2)}]

=x[{(x + 2)(x-1)}]

=x×(x + 2)×(x-1)
GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴ the GCD of x²-1, x²-2x + 1, x³ + x²-2x is (x-1)