SOLUTION: I need help on how to factor this expression. (x-y)^2+3(y-x)^3

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Question 515514: I need help on how to factor this expression.
(x-y)^2+3(y-x)^3
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor this expression.
(x-y)^2+3(y-x)^3
------------------
Note: y-x = -(x-y)
-----------------------
(x-y)^2+3(y-x)^3
---
(x-y)^2 + 3(-(x-y))^3
----
(x-y)^2 - 3(x-y)^3
---
Factor:
(x-y)^2[1 - 3(x-y)]
---
(x-y)^2[-3x+3y+1]
==========================
Cheers,
Stan H.
==================

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
(x-y)² + 3(y-x)³

Notice that (x-y) and (y-x) are opposite differences,
we can write either one in terms of the other. Let's
write (x-y) in terms of (y-x)

(x-y) = 
Write the two terms in the opposite order:
(-y+x) = 
factor out -1:
-1(y-x)


replace (x-y) by -1(y-x) using brackets

[-1(y-x)]² + 3(y-x)³

Remove the brackets by squaring each of the two factors within

(-1)²(y-x)² + 3(y-x)³

and since (-1)² is 1

(y-x)² + 3(y-x)³

Now we can factor out (y-x)²

(y-x)²[1 + 3(y-x)]

Remove the parentheses inside the bracket:

(y-x)²[1+3y-3x]

Chance brackets to parentheses:

(y-x)²(1-3y+3x)

Edwin