If $x = ab^3$ and $y = a^3b$, where $a$ and $b$ are prime numbers, then $ ext{HCF}(x, y) - ext{LCM}(x, y)$ is equal to:

Question

If $x = ab^3$ and $y = a^3b$, where $a$ and $b$ are prime numbers, then $	ext{HCF}(x, y) - 	ext{LCM}(x, y)$ is equal to:

Accepted Answer

Step 1: $	ext{HCF}(ab^3, a^3b) = ab$, $	ext{LCM}(ab^3, a^3b) = a^3b^3$.
$	ext{HCF} - 	ext{LCM} = ab - a^3b^3 = ab(1 - a^2b^2) = ab(1 - ab)(1 + ab)$

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