Find the HCF and LCM: 4(a⁴ - a²b²), 6(a³b - ab³), 96(a³b + b⁴)

Solution:
Here,

1st expression: $4(a^4 - a^2b^2)$
= $4a^2(a^2 - b^2)$
= $2×2×a^2(a +b)(a -b)$

2nd expression: $6(a^3b - ab^3)$
$= 6ab(a^2 - b^2)$
$= 2×3×ab(a +b)(a -b)$

3rd expression: ${96(a^3b +b^4)}$
$= 96×b(a^3 + b^3)$
$= 2×3×16×b(a+b)(a^2 - ab + b^2)$

Now,

Highest Common Factor = common factors only = $2(a+b)$

Lowest Common Multiples = common factors × rest factors
$= 2(a+b) × 3×16×ab (a-b)(a^2-ab+b^2)$
$= 96 ab (a -b)(a^3 + b^3)$