Ok, I'm supposed to factor this, and the steps are kind of confusing me....?

Question

I'm in Algebra....and have to factor...

x (squared) + 4xy + 4y (squared) - 16....

PLEAS HELP ME!!!

Answer 1

This is the answer...

(x+2y+4)(x+2y-4)


this is why...
x(x+2y-4) = x^2+2xy-4x
+2y(x+2y-4) = +2xy+4y^2-8y
+4(x+2y-4) = +4x+8y-16

add all... x^2 - 4x + 4x + 2xy + 2xy -8y + 8y + 4y^2 - 16
cancels... -4x + 4x, -8y + 8y
Add... +2xy + 2xy = 4xy
back to anwser... x^2 + 4xy + 4y^2 - 16

Answer 2

for this type of problem you "Complete the Square"

x^2 + 4xy + 4y^2 -16 = 0

1) bring the constant to the other side

x^2 + 4xy +4y^2 = 16

2) take the linear term and divide by 2. (the stuff next to x).

in this case the linear term is 4xy and the stuff next to x is 4y:
so we get 2y.

3) Write the stuff on the Left Hand Side of the equal sign in a different way, that is you simply write:

(x + 2y)^2

4) expand (foil) this to see what you get, in this case we get:

(x + 2y)^2 = x^2 + 4xy + 4y^2

and we know this is equal to 16 so it must be the case that

(x + 2y)^2 = 16

5) now take the square root of both sides (remember you'll get plus and minus)

x + 2y = 4 --> x + 2y -4 =0
and
x + 2y = -4 --> x + 2y +4 =0

you use these to put original equation in factored form:

(x + 2y -4)(x + 2y +4) = 0

****
Extra: The important part of completing the square is at steps 3 & 4. after you divide by 2 you must expand (as in step 4) to make certain that equality will still be true. if it isn't then you have to account for the difference on the Right Hand Side.

Answer 3

So, you want to factor

x^2 +4xy +4y^2 -16

So, you've got x's, y's and a constant.

(x +2y - 4) (x +2y +4) Using FOIL (first, inner,outer, last)

x^2 +2xy +4x +2xy +4y^2 +8y -4x -8y -16

Collect terms

x^2 +4xy +4y^2 -16

You need to have equal factors for the y^2 term and the end factor 16. This creates the difference of two squares to make terms drop out - like x^2-9 is factored by (x+3)(x-3).

Answer 4

(x+2y)^2-4^2
(x+2y+4)(x+2y-4)

It's that simple..