1. ## Trinomial product shortcut

Hello, I am having trouble with this problem:

Find the product of (x+y-2) and (x+y+2)

Now, obviously I can use the, so to speak, "old fashion" way by foiling it. But they say in the solution that I can use a special product and rewrite it as:

[(x+y)-2][(x+y)+2]

And furthermore be written as:

(x+y)^2-2^2

Could someone please explain how they are doing this?

Thank you very much.

2. ## Re: Trinomial product shortcut

Originally Posted by Bashyboy
Hello, I am having trouble with this problem:
Find the product of (x+y-2) and (x+y+2)
Just do it: $(x+y-2)(x+y+2)=(x)(x)+(x)(y)+(x)(2)+(y)(x)+(y)(y)+(y)(2 )+(-2)(x)+(-2)(y)+(-2)(2)~.$

3. ## Re: Trinomial product shortcut

Originally Posted by Bashyboy
Hello, I am having trouble with this problem:

Find the product of (x+y-2) and (x+y+2)

Now, obviously I can use the, so to speak, "old fashion" way by foiling it. But they say in the solution that I can use a special product and rewrite it as:

[(x+y)-2][(x+y)+2]

And furthermore be written as:

(x+y)^2-2^2

Could someone please explain how they are doing this?

Thank you very much.
You should know that $\displaystyle (a - b)(a + b) = a^2 - b^2$ from the Difference of Two Squares rule.

Here they have let $\displaystyle a = x + y$ and $\displaystyle b = 2$.