How do you factor x² + xy - 6y² ?

x² + xy - 6y²

=

- 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.

(x + 3y)(x - 2y)

= x(x) + x(-2y) + 3y(x) + 3y(-2y)

= x² - 2xy + 3xy - 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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