Help my brain is overloading!!!

Given f(x)= x^2-2x-1 find f(x^2+3)

I got x^4-2x^2+2

but its x^4-4x^2+2

Question

Help my brain is overloading!!!

Given f(x)= x^2-2x-1   find   f(x^2+3)

I got x^4-2x^2+2

but its x^4-4x^2+2

anonymous · Answer

can you tell me why its 4 rather than 2?

anonymous · Answer

probably algebra

anonymous · Answer

this problem has been bothering me for the last 2 hours im so frustrated

anonymous · Answer

$$f(x)= x^2-2x-1$$$$ f(x^2+3) =(x^2+3)^2-2(x^2+3)-1$$

anonymous · Answer

it isnt worth that much of your time

anonymous · Answer

yea thats exactly what i did and i got my answer

anonymous · Answer

course i didn't do it, maybe your answer is correct
shall we check?

anonymous · Answer

but i don't understand why its a 4x^2 rather than 2x^2

anonymous · Answer

$$(x^2+3)^2=x^4+6x^2+9$$

anonymous · Answer

when you subtract the $2x^2$ from the second term you will be left with $4x^2$
did you forget to square correctly?

anonymous · Answer

why is it 6x^2

anonymous · Answer

tsk tks,  you deserve to lose two hours if you forgot how do square something
please don't tell me you think $(a+b)^2=a^2+b^2$ when it is really 
$$(a+b)^2=a^2+2ab+b^2$$

anonymous · Answer

wait but why do you do 2ab tho? i don't understand .... its not like we're factoring anything here

anonymous · Answer

you don't "do" anything, you multiply 
$$(x^2+3)^2=(x^2+3)(x^2+3)=x^4+3x^2+3x^2+9=x^4+6x^2+9$$

anonymous · Answer

wow......

anonymous · Answer

okay im super stupid....

anonymous · Answer

wow...... *facepalm* okay thanks ...

anonymous · Answer

yw