SOLUTION: How do I factor the trinomial and GCF of.. x^2-4xy-77y^2 I started with (x-) (x-) I don't know what to do next.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I factor the trinomial and GCF of.. x^2-4xy-77y^2 I started with (x-) (x-) I don't know what to do next.      Log On


   



Question 439938: How do I factor the trinomial and GCF of..
x^2-4xy-77y^2
I started with (x-) (x-)
I don't know what to do next.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Key things to notice are;
(1)
The fact that the signs have the pattern +ax%5E2+-+b%2Ax%2Ay+-+c%2Ay%5E2+
tells me that the factors will look like %28x+%2B+y%29%2A%28x+-+y%29 (with coefficients)
and that the +-x%2Ay+ of the factoring will be greater than the +%2Bx%2Ay+
to give me the +-b%2Ax%2Ay+ middle term of the equation.
(2)
The fact that +77+=+7%2A11+ and +11+-+7+=+4+ tells me where the
-4 in the middle term comes from.
--------------------
With these observations, I can try to factor it:
+x%5E2+-+4x%2Ay+-+77y%5E2+=+%28+x+%2B+7y+%29%2A%28+x+-+11y+%29+
Notice the 11 has to have the (-) sign, and
the difference of 11 and 7 has to be 4