How do I factor #x^2-10xy-11y^2#?

1 Answer

Answer:

#(x-11y)(x+y)#

Explanation:

We have

#x^2-10xy-11y^2#

And we're looking to set up factors.

Looking at the expression, we know we need #x# terms so that they will multiply and make a #x^2#. We also need #y# terms, one being an #11y# and the other being #y# and one of them being negative.

So we have, in part:

#(xpmY)(xpmY)#, where #Y# is our #y# terms, and we also have:

#(Xpm11y)(Xpmy)#, where #X# is our #x# terms

We can now see that we also need an #-10xy# term, and we can get that by having #-11y, y# terms. Putting it altogether:

#(x-11y)(x+y)#