Question

If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) – LCM (x, y)] is equal to ______.

Options

• 1 − a³b³

• ab (1 − ab)

• ab − a⁴b⁴

• ab (1− ab) (1 + ab)

Answer 1

If x = ab³ and y = a³b, where a and b are prime numbers, then [HCF (x, y) – LCM (x, y)] is equal to ab (1− ab) (1 + ab).

Explanation:

x = ab³ and y = a³b

LCM (x, y) = a³b³

HCF (x, y) = ab

Now, [HCF (x, y) – LCM (x, y)]

= ab − a³b³

= ab (1 – a²b²)

= ab [1² – (ab)²]

= ab (1 – ab) (1 + ab)