Q. 3 K3.5( 10 Votes )
Let’s find G.C.D of the following algebraic expression:
4x2-1, 8x3-1, 4x2-4x + 1
Answer :
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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