Question 109879
First off, what two numbers multiply to -6 (the last coefficient) but add to -1 (the middle coefficient)? It turns out that -3 and 2 multiply to -6 but add to -1.


So replace the middle term of {{{b^2-ab-6a^2}}} with {{{-3ab+2ab}}} to get  {{{b^2-3ab+2ab-6a^2}}} 


Now let's factor {{{b^2-3ab+2ab-6a^2}}} by grouping



{{{(b^2-3ab)+(2ab-6a^2)}}} Group like terms



{{{b(b-3a)+2a(b-3a)}}} Factor out the GCF of {{{b}}} out of the first group. Factor out the GCF of {{{2a}}} out of the second group



{{{(b+2a)(b-3a)}}} Since we have a common term of {{{b+-3a}}}, we can combine like terms


So {{{b^2-3ab+2ab-6a^2}}} factors to {{{(b+2a)(b-3a)}}}


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Answer:


This means {{{b^2-ab-6a^2}}} factors to {{{(b+2a)(b-3a)}}} also



Notice how {{{(b+2a)(b-3a)}}} foils back to {{{b^2-3ab+2ab-6a^2}}} which simplifies to {{{b^2-ab-6a^2}}}. So this verifies our answer.