How Do You Solve f(x-y) - f(x) in Algebra II?

[DukeGuy123]

I've got a question maybe you guys can answer.

I'm in Algebra II and I was given a question that was worded like this:

"If f(x) = x², then find f(x-y)-f(x)."

Can someone help me? I don't really know how to solve it...

-DukeGuy123

 

[lurflurf]

f(x-y)-f(x)=(x-y)^2-x^2
one would then likely be expected to expand and simplify

 

[DukeGuy123]

That's not one of the valid answer choices...

It's one of these four (it's multiple choice):

A) 2x
B) x²-2xy+y²
C) -2xy+y²
D) 2xy-y²

Thanks for your help, but I would like to get an answer that is Correct and WITH WORK.

I really don't know how to solve this.

 

[DukeGuy123]

lurflurf, did you check the answer choices?

Which answer choice would that be? And is there a more detailed way you can explain it, because I still don't get it.

Can you show it like step-by-step or something?

 

[lurflurf]

so f(x) = x² means that whenever you see f(*) were * is some expresion you replace it by *²
so if you have
f(x-y)-f(x)
it gives
(x-y)²-x²
you should be able to expand (x-y)² using foil or (a+b)²=a²+2 a b+y²
then cancel

 

[Nickcanada]

so f(x) = x² means that whenever you see f(*) were * is some expresion you replace it by *²
so if you have
f(x-y)-f(x)
it gives
(x-y)²-x²
you should be able to expand (x-y)² using foil or (a+b)²=a²+2 a b+y²
then cancel

yup! f(x) =x² shows you how the function is affecting the variable

if the variable inside the parentheses is something other than x, it is affected the same way that x would be as long as the function is still f, and not some other function.

 

[Mark44]

Anakin_k, it is against the policy in this forum to provide complete solutions to a poster's problems.

 

[HallsofIvy]

lurflurf, did you check the answer choices?

Which answer choice would that be? And is there a more detailed way you can explain it, because I still don't get it.

Can you show it like step-by-step or something?

Lurflurf Suggested you expand (x-y)²- x². Have you done that yet?

 

[sportsstar469]

Lurflurf Suggested you expand (x-y)²- x². Have you done that yet?

in case you didnt know (x-y)^2 is really (x-y)(x-y)
with that knowledge you should be able to solve (x-y)(x-y) -x^2 just foil it all out!
(x^2-xy-xy+y^2)-x^2
combine like terms (x^2-2xy-y^2)-x^2
the x'2s cancel oiut leaving you with -2xy-y^2
factor out a -y -y(2x+y)

if i didnt totally screw this up there's your answer.

 

[sportsstar469]

ah ok hear x2(x-y)-x2(x)-------x3-xy-x3=xy

you don't multiply x-y times x squared. x-y IS x in this problem times the whole thing squared. that's what f(x)=x^2 is saying. its defining the function/ you did not substitute for x you just multiplied numbers by sx.