How do you factor by grouping #r(p^2 + 5) - s(p^2 + 5)#?

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Answer 1 · 2018-03-14T06:11:59

The factored expression is #(r-s)(p^2+5)#.

Imagine that the #(p^2+5)# terms are their own variable. It might actually be easier to do that for a few steps.

Substitute out #(p^2+5)# for #u#. Then, we can factor like we already know how to:

#color(white)=r(p^2+5)-s(p^2+5)#

#=ru-su#

#=(r-s)*u#

Now, put back in #(p^2+5)# for #u# (don't forget the paretheses):

#color(white)=(r-s)*u#

#=(r-s)(p^2+5)#

That's how you factor by grouping. Hope this helped!