Factoring with 2 Variables
You will follow all your same factoring rules.
1) Look for a GCF.
2) Choose whether it is Case I, DOTS, or CASE II and proceed.
Remember: All the rules of factoring quadratics come from what will result when you
FOIL check the two binomials:
Example:
x2 – xy – 6y2
Usually, we start off with (x + )(x - ). We do this because we know when we FOIL,
with the F (first), we need x ∙ x to get us x2. Then we follow the rest of the rules.
This one is just a little different. Now we’ll start with (x + __ y)(x - __ y), because not
only do we need the x ∙ x to get x2, we’ll need a y ∙ y to get us the y2 we need at the end of
the trinomial when we do the L (last).
Once you have that you can proceed. We will need factors of 6 with a difference of 1.
The factors of 3 and 2 satisfy that and we will put the 3 with the minus sign because that
is where the 1st sign tells us to put the bigger #.
(x + 2y)(x - 3y)
Examples:
1) x2 – 13xy + 40y2
2) c2 + 3cd – 18d2
3) s2 – 121t2
4) 3u2 + 33uv + 84v2
5) 5a2 – 30ab – 135b2
6) 81f 2 – 16g2
7) 8r2 – 200s2
8) 16x2 – 144y2
9) 100w2 – 25x2
10) g2 – 5gy – 50y2
11) 6x2 – 5xy – 4y2
12) 5w2 + 12wx + 4x2