Q3 E of 42 Page 136

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

a2-1, a3-1, a2 + a-2


Factors of a2-1=(a + 1)(a-1)

Factors of a3-1=(a-1)(a2 + a + 1) … (from properties)
Factors of a2 + a-2


=(a2 + a-2)


=(a2 + 2a-a-2)


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


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


=(a + 2)×(a-1)


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


∴the GCD of a2-1, a3-1, a2 + a-2 is (a-1)


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