Q3 K of 42 Page 136

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

4x2-1, 8x3-1, 4x2-4x + 1


Factors of 4x2-1

=(2x + 1)(2x-1) … (Using a2-b2=(a + b)(a-b))


Factors of 8x3-1


=(2x-1)(4x2 + 2x + 1) … (using a3-b3=(a-b)(a2 + ab + b2)


Factors of 4x2-4x + 1


=(2x-1)2 … (from properties)


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


∴ the GCD of 4x2-1, 8x3-1, 4x2-4x + 1 is (2x-1)


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