Question

Prove (x+y)(x+y)=x^2+2xy+y^2. Could you please check our work? I'm working with a partner on this and I have to be sure we are correct. Thank you.

Answer 1

x/y + y/x = 2 Given.
x≠0 and y≠0 Because then the original question would be dividing by zero.
xy≠0 Because neither factor is zero.
(xy) (x/y + y/x) = (xy) 2 Multiply both sides of given equation by (xy); we can do this because we are not multiplying by zero.
x2 + y2 = 2xy Simplify.
x2 - 2xy + y2 = 0 Make one side zero.
(x-y)2 = 0 Factor it.
(x-y) = 0 Take the square root of both sides.
x = y. Solved.

Answer 2

for your first part, all I see are boxes instead of variables (see attached)

Answer 3

Thank you for telling me. Just one sec.

Answer 4

you see now?

Answer 5

ok much better

Answer 6

I also think I could use FOIL with the left side to make it equal the right side. That seems the simplest to me.

Answer 7

yes you can use FOIL or the distributive property go from (x+y)(x+y) to x^2+2xy+y^2

Answer 8

easy:
(x+y)*(x+y)=x^2+xy+yx+^2=x^2+2xy+y^2

Answer 9

simplify FOIL it

Answer 10

you can also use the box method as a visual way to do it

Answer 11

To be honest, I'm not sure how the two parts are connected. I don't see (x+y)(x+y) anywhere in the second part. I guess it's similar to (x-y)^2 = (x-y)(x-y) = x^2-2xy+y^2

Answer 12

Could you show me the box method please?

Answer 13

sure

we have (x+y) times (x+y)

there are 2 terms in each parenthesis

so we will have a 2x2 box like this

Answer 14

along the left and top edges we place the terms from x+y and x+y