-36a^2b+21ab^2-3b^3
First note they all have a -3b in them so factorise that out first:
-3b(12a^2 - 7ab + b^2)
Then think of it like a regular trinomial.
What two numbers multiple to give 12 and add to give -7.
Obviously -3 and -4.
So it is:
-3b(12a^2 - 3ab - 4ab + b^2)
=-3b(3a(4a-b) - b(4a-b))
=-3b(3a-b)(4a-b)
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Verified answer
First note they all have a -3b in them so factorise that out first:
-3b(12a^2 - 7ab + b^2)
Then think of it like a regular trinomial.
What two numbers multiple to give 12 and add to give -7.
Obviously -3 and -4.
So it is:
-3b(12a^2 - 3ab - 4ab + b^2)
=-3b(3a(4a-b) - b(4a-b))
=-3b(3a-b)(4a-b)