Question

if x^2-y^2=12 and x-y=4 what is the value of x^2+2xy+y^2

a. 3
b. 8
c. 9
d. 12
e. 16

Answer 1

you could factor x^2-y^2
and then use what x-y is equal to to find x+y

Answer 2

then recall x^2+2xy+y^2 can be written as (x+y)^2

Answer 3

Erm....

Well here's what I did so far...

I did (x-y)^2 and got x^2 - 2xy + y^2 = 16

I don't know what else to do

Answer 4

well can you try what I said?

Answer 5

x^2-y^2 can be factored

Answer 6

it is a difference of squares

Answer 7

you are given the value of x-y
this will allow you to find x+y

Answer 8

and then all you have to do after finding x+y is find (x+y)^2

Answer 9

So have you factored x^2-y^2 yet?

Answer 10

(x-y)(x+y)

Answer 11

\[x^2-y^2=12 \\ (x-y)(x+y)=12 \\ \text{ you are given } x-y=4 \\ \text{ just plug in } \\ 4(x+y)=12\]

\[\text{ and you want to find } (x+y)^2\]

Answer 12

Ahh!! Now I understand it. Thank you!

Answer 13

k great