How do you factor #5x^2 + 41xy - 36y^2#?

Question

1430 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-20T14:50:17

The coefficients of #x^2# and #y^2# are, respectively, #5# and #-36#. The product #5(-36)=-180#, which, can be factored as #(-4)(45)#.

So, we can now rewrite #5x^2+41xy-36y^2# as

#5x^2-4xy+45xy-36y^2#

Now, we can factor this by two groups:

#x(5x-4y)# and #9y(5x-4y)#

We can see that the parenthesis are shared by the two factors. It becomes clearer when we rewrite:

#x(5x-4y)+9y(5x-4y)=(x+9y)(5x-4y)#