Question

please help me factor:

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

Answer 1

Why do you believe you can factor it?

Answer 2

it's on a worksheet

Answer 3

Fair enough. What's your plan?

Answer 4

i have the answer key, but when i do it. i get it wrong

Answer 5

x^2+2xy_y^2 factors to (x+y)^2 and then factor 2 out of 2x+2y-8...but it;s after that

Answer 6

it's wrong*

Answer 7

Okay, then why not do it in a way that works? As in, try something else.

Answer 8

on the answer key, it only factored out 2 for 2x+2y only? i dont know why. Can you explain to me?

Answer 9

If we are going to get x^2, y^2, xy and a constant term, it has to factor like this:

(ax+by+c)(dx+ey+f)

Since we'll need a coefficient of 1 on x^2, then a = d = 1

(x+by+c)(x+ey+f)

Since we'll need a coefficient of 1 on y^2, then b = e = 1

(x+y+c)(x+y+f)

By a little luck, maybe, this also produces 2xy.

Since we'll need a constant term of -8, then c*f = -8
The coefficients on x and y suggest also that c + f = 2

Can you solve for c and f?

Answer 10

If you like, we can treat it like any other quadratic expressions.

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

(x^2 + 2xy + y^2) + (2x + 2y) - 8

(x + y)^2 + 2(x + y) - 8

If this said, z^2 + 2z - 8, could you factor it?

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