# Thread: No idea how to do this

1. ## No idea how to do this

$\displaystyle (x - y)^2 + 13(x - y) + 42$

Please someone help me or something. I have no idea how to do this at all.
Like what do I do when its $\displaystyle (x - y)^2$?

2. Originally Posted by lax600
$\displaystyle (x - y)^2 + 13(x - y) + 42$

Please someone help me or something. I have no idea how to do this at all.
Like what do I do when its $\displaystyle (x - y)^2$?
I'm guessing you want to expand this.

$\displaystyle (x - y)^2 = x^2 - 2xy + y^2$, for starters.

3. I need to factor it... so I still expand it?

4. $\displaystyle (x - y)^2 + 13(x - y) + 42$ is about as factored as it gets. One thing you can do:

$\displaystyle (x - y + 13)(x - y) + 42$

$\displaystyle (x - y)^2 - 13(x - y) + 42$

if $\displaystyle (x - y)^2 - 14(x - y) + 49$

$\displaystyle (x - y)^2 - 2*7*(x - y) + 7^2$

a =$\displaystyle (x - y)^2$
b =$\displaystyle 7$

$\displaystyle (x - y)^2 - 13(x - y) + 42 = [(x - y)^2 - 14(x - y) + 49] ={[(x - y) - 7]^2 + [(x - y) - 7]}$
$\displaystyle =(x - y -7){x - y - 7} =(x - y - 7)(x - y - 6)$

6. Originally Posted by lax600

$\displaystyle (x - y)^2 - 13(x - y) + 42$

if $\displaystyle (x - y)^2 - 14(x - y) + 49$

$\displaystyle (x - y)^2 - 2*7*(x - y) + 7^2$

a =$\displaystyle (x - y)^2$
b =$\displaystyle 7$

$\displaystyle (x - y)^2 - 13(x - y) + 42 = [(x - y)^2 - 14(x - y) + 49] ={[(x - y) - 7]^2 + [(x - y) - 7]}$
$\displaystyle =(x - y -7){x - y - 7} =(x - y - 7)(x - y - 6)$
yeah, that's right. Just substitute $\displaystyle t = x-y$ and you have $\displaystyle t^2 - 13t + 42$ which easily factors to $\displaystyle (t - 6)(t - 7)$. I should have been thinking along those lines.

7. oh