SOLUTION: Factor x^2+(x-y)^2-2x*(x-y) Thank you, this question is not from text book

Question 127254: Factor x^2+(x-y)^2-2x*(x-y) Thank you, this question is not from text book
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Rearrange the terms

Now let . So our equation becomes

Notice how I replaced each with z

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 1 respectively.

Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient -2? Let's list all of the factors of 1:

Factors of 1:
1

-1 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 1
1*1
(-1)*(-1)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First Number Second Number Sum
1 1 1+1=2
-1 -1 -1+(-1)=-2

From this list we can see that -1 and -1 add up to -2 and multiply to 1

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

note: is equivalent to since the term occurs twice. So also factors to

So factors to

Remember, we let . So replace each z with

Combine like terms

Square -y to get

------------------------------------

Answer:

So factors to
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Factor

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