Question #73265

1 Answer
Jun 1, 2017

Answer:

#(x+y)(2x-y)#

Explanation:

Treat this like a quadratic of the form #ax^2+bx+c#.

#a=2#
#b=y#
#c=-y^2#

Now, to factor, we need to find 2 factors of #ac# which add up to #b#.

#ac = 2(-y^2) = -2y^2#

We can use #2y# and #-y#, since #2y(-y)=-2y^2# and #2y+(-y)=y#. This satisfies both conditions of multiplying to make #ac# and adding up to #b#.

Our factored form will look like this:

#a(x+"factor 1"/a)(x+"factor 2"/a)#

#2(x+(2y)/2)(x+(-y)/2)#

#2(x+y)(x-y/2)#

#(x+y)(2x-y)#

Final Answer