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

8(x²-4),12(x³ + 8),36(x²-3x-10)

Factors of 8(x²-4)=2×2×2×(x-2)×(x + 2)

Factors of 12(x³ + 8)

=2×2×3×(x + 2)×(x²-2x + 4)

… ((x³ + 8)= (x + 2)×(x²-2x + 4) from properties)

Factors of 36(x²-3x-10)

Factors of (x²-3x-10)

=(x²-5x + 2x-10)

=x(x-5) + 2(x-5)

=(x + 2)(x-5)

Factors of 36(x²-3x-10)=2×2×3×3×(x + 2)×(x-5)

GCD is the greatest common divisor, which is equal to the product of all the common divisors.

∴the GCD of 8(x²-4),12(x³ + 8),36(x²-3x-10) is 4(x + 2)