Extracting the common factors from each term:
color(white)("XXX"){:
(ul(36),ul(66),ul(210)," | ",6),
(ul(a^3),ul(a^2),ul(a)," | ",a),
(ul(b^2),ul(b^3),ul(b^4)," | ",b^2)
:}
giving
color(white)("XXX")(6ab^2)(6a^2+11ab-35b^2)
Looking for integer (we are optimists) coefficients as factors for (6a^2+11ab-35b^2)
color(white)("XXX"){:
(ul("factors of 6"),ul("factors of 35"),ul("difference of cross product")),
(1,5,),
(ul(6),ul(7),ul(23)),
(1,7,),
(ul(6),ul(5),ul(37)),
(2,5,),
(ul(3),ul(7),ul(1)),
(2,7,),
(ul(3),ul(5),ul(11))
:}
...and we have found a set that gives us the coefficient of the middle term!
It only remains to figure out the positive/negative signs to give +11
(6ab^2)(2a-7b)(3a+5b)
