Confused with algebra problem?

Question

Confused with algebra problem?

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

this is what my book does to solve this problem:

[(x+y)-2][(x+y)+2]=(x+y)^2 -2^2(squared)=x^2+2xy+y^2-4(ans. for multiplying polynomial)..Can you please tell me what rule in Algebra lets me do this? I never knew you could bracket out two variables like that ..please explain!!

Answer 1

sorry I suck at algebra in school and still to this day, and in all of my years I never used it to me it is just a waste of time unless your going to be some-kind of rocket scientist  

Answer 2

Think of it as replacing (x+y) with z

(x+y-2)(x+y+2) = ((x+y)-2)((x+y)+2) = (z-2)(z+2) = z² - 4

Now replace z with (x+y) and expand:

z² - 4 = (x+y)² - 4 = x² + 2xy + y² - 4

Hope that helps you see the trick.

Answer 3

I don't like that. Try following this.

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

if we let a=(x+y) then

(a - 2)(a + 2) then

a² -2a + 2a - 4

a² - 4 ,

what is a² , well a=(x+y) so

a² = (x+y)² = (x+y)(x+y) = x² + 2xy + y² , so then

a² - 4 =

x² + 2xy + y² - 4

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Don't take advise from losers. Algebra is needed many things, but calculus is needed for rocket science.