Question

Factor completely x^(2) + 2xy + y^(2) - a^(2).

Answer 1

@aimmeBgood i have no idea how to solve this so i'm here to learn!! And @satellite73 most likely understands this so i'm here to understand too! :)

Answer 2

\[x^2+2xy+y^2\] is a perfect square
it is \((x+y)^2\)

Answer 3

ohhh you take it apart? into pieces? and factor what you can?

Answer 4

anytime you see something that looks like \(a^2+2ab+b^2\) you have a perfect square
so now you can start with
\[(x+y)^2-a^2\] which is itself the difference of two squares

Answer 5

oh and i see how you got (x+y)^2 for the first three terms... :) so would the answer be

Answer 6

you can go further

Answer 7

ohhh :) how?

Answer 8

because now you have the difference of two squares
\[A^2-B^2=(A+B)(A-B)\]

Answer 9

but where does the 2 go? i dont understand.

Answer 10

replace \(A\) by \((x+y)\) and \(B\) by \(a\)

Answer 11

the 2 does not "go" anywhere, it is hidden in \((x+y)^2\)

Answer 12

if you multiply out you get \((x+y)^2=(x+y)(x+y)=x^2+xy+yx+y^2=x^2+2xy+y^2\)

Answer 13

your final answer should look like \((x+y+a)(x+y-a)\)

Answer 14

that makes sense. i get it now. thanks

Answer 15

yw

Answer 16

oh wow! that's cool :) that makes sense!! :) @satellite73 strikes again! :) And thanks for the explanation! (even tho it wasn't my question, i understand it now!) :D