I have absolutely no clue how to solve this PLEASE HELP. I'm suppose to factor this... but how??
x(2y-x)^2 + 2x^2 (x-2y)

Step-by-step explanation:

We want to factor the following expression:

First, notice that both of the terms have an x. Thus, let's factor out the x first:

Now, notice the similarity between (2y-x) and (x-2y). If we multiply either of them by a negative, they will be the same.

Therefore, we can factor out a negative from (x-2y). This will give us:

Since multiplication is commutative:

Now, we can factor out the (2y-x):

And we can simplify this to get:

Alternate Method:

Starting from here:

We can factor out a negative from the (2y-x)² term. This yields:

Since -1 squared is positive, we can simplify:

Now, we can factor out the (x-2y):

Simplifying gives:

While this looks different, they are exactly the same. If we factor out a negative from both the second and third term, we get:

The negatives will cancel, leaving us with:

This is exactly the same as what we acquired previously.

Therefore, both answers are correct.