SOLUTION: How do you factor (x^2+2xy+y^2)-4w^2?

Question 183267: How do you factor (x^2+2xy+y^2)-4w^2?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

First, we need to factor

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

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

So the original expression becomes

Rewrite as

Notice how we now have a difference of squares. Remember, the difference of squares formula is

In this case, and

Now plug them in the formula to get:

==================================================

Answer:

So this means that factors to

Equivalently, this means that factors to
RELATED QUESTIONS
how do you factor... (answered by ReadingBoosters)

How do I graph x^2+2xy+y^2=1? (answered by Fombitz)

Factor: x^2+2xy+y^2... (answered by Alan3354)

factor: 2xy - 8x^(2)y +... (answered by Alan3354)

factor each polynomial... (answered by 303795)

Factor completely: x^2 - 2x + y^2 + 2y - 2xy -... (answered by mananth,stanbon)

Using the "ac method" how do I factor 8x^2-2xy-y^2... (answered by Edwin McCravy)

please factor completely thefollowing: {{{x^2-y^2}}} {{{x^2-2xy+y^2}}}... (answered by pushpaharan)

How do you factor things like 2xy^2 or... (answered by Alan3354)