Factor x² + xy - 6y²

How do you factor  x² + xy - 6y² ?

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x² + xy - 6y²

=  (x + 3y)(x - 2y)

- The first terms, x and x, multiply to make x².
- The last term coefficients of the two binomials multiply to make the last coefficient, -6, and add to make the middle
coefficient, 1.  Also, the last terms have y attached to them, due  to the y in the middle term and the last term.

Check with the FOIL method / distributive property:
(x + 3y)(x - 2y)
=  x(x) + x(-2y) + 3y(x) + 3y(-2y)
=  x² - 2xy + 3xy - 6y²
=  x² + xy - 6y²


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