How do you factor x² + xy - 6y² ?
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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