If u(x) = (x – 1)

u(x) = (x – 1)2

= (x – 1) (x – 1)

v(x) = (x2 – 1)

= (x + 1) (x – 1)

LCM of u(x) and v(x) = (x – 1)2 (x + 1)

HCF of u(x) and v(x) = (x – 1)

u(x) × v(x) = (x – 1) (x – 1) × (x2 – 1)

= (x2 – 2x + 1) × (x2 – 1)

= x4 – 2x3 + x2 - x2 + 2x – 1

= x4 – 2x3 + 2x – 1

HCF × LCM = (x – 1)2 (x + 1) × (x – 1)

= (x2 – 2x + 1) (x2 – 1)

= x4 – 2x3 + x2 - x2 + 2x – 1

= x4 – 2x3 + 2x – 1

So it is observed that HCF × LCM = u(x) × v(x).

Hence Proved.

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