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

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Answer 1 · 2018-03-14T06:11:59

The factored expression is $(r - s) (p^{2} + 5)$ $(r-s)(p^2+5)$ .

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

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

$= r (p^{2} + 5) - s (p^{2} + 5)$ $color(white)=r(p^2+5)-s(p^2+5)$

$= r u - s u$ $=ru-su$

$= (r - s) \cdot u$ $=(r-s)*u$

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

$= (r - s) \cdot u$ $color(white)=(r-s)*u$

$= (r - s) (p^{2} + 5)$ $=(r-s)(p^2+5)$

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

How do you factor by grouping r(p2+5)−s(p2+5)r(p^2 + 5) - s(p^2 + 5)?