Is my Algebra 1 key incorrect or am I?

[Ann.without.an.e]

Problem is this.... Assume ^2 is to the power of 2 since I can't find a symbol for it

 

F(x) = x^2+2x+2

find f(m-1)

 

I get this (I will show my work :)

 

f(m-1) = (m-1)^2 + 2(m-1) + 2

 

m^2+1+2m-2+2

 

m^2+2m+1

 

 

My key says the answer should be

 

m^2+1

 

Is it incorrect or did I go wrong somewhere? Granted, I am NOT an algebra gal so I could most definitely be incorrect, lol.

 

Thanks ya'll

[Dana]

Problem is this.... Assume ^2 is to the power of 2 since I can't find a symbol for it

 

F(x) = x^2+2x+2

find f(m-1)

 

I get this (I will show my work :)

 

f(m-1) = (m-1)^2 + 2(m-1) + 2

 

 

You're correct here.

Next line is wrong. Exponents don't distribute over addition or subtraction. You have to use square of difference formula or write out (m-1)(m-1) and distribute.

 

You should get next....

m^2 -2m +1 +2m-2+2

m^2+1

[Jann in TX]

You made a classic mistake when you squared the (m-1) think of it as (m-1)(m-1) and it should be m^2-2m+1 not m^2-1 (you left out midle term!)

[Matryoshka]

The answer key is right. Your mistake is trying to distribute the exponent in the first term over subtraction. (m-1)^2 does not equal m^2+1, it is the whole expression squared, which is (m-1)(m-1), which distributes out with FOIL to m^2-2m+1. The other terms your dealt with properly, so that would be

 

(m^2-2m+1) + (2m-2) + 2, which reduces to m^2+1

[Ann.without.an.e]

Aha, thank you. I told you that I am NOT a math gal. DD rarely misses an answer on a test so I thought the key was incorrect. When I showed her your post she immediately knew what she did wrong. Thank you so much! Ya'll rock, but you know that already :)

[kiana]

This error is so common that it's often called 'The freshman's dream' or 'the freshman's mistake' -- so she's in good company. If she can manage to consistently remember not to do this, she'll be ahead of about 50% of college students. (seriously)

[EKS]

Another vote for the answer key.