Question 83585
The given expression is 2a^3-52a^2b+96ab^2

As a is common to all the terms, remove it out.

= a(2a^2 - 52ab + 96b^2)

Now find 2 numbers whose product = 2 x 96 = 192 and whose sum = - 52

On trying out, w find the numbers as - 48 and - 4

= a(2a^2 - 4ab - 48ab + 96 b^2) [splitting the middle term]

= a[2a(a - 2b) - 48b(a - 2b)]

= a(a - 2b) ( 2a - 48b)

= a(a - 2b)*2(a - 24 b)

= 2a(a - 2b)(a - 24b)