If the expression f^2+g^4-2f+1 is rewritten in the form a^2 + (g^2) ^2, what must be the value of a?

Answer: √ (f^2 - 2f + 1) = a

Step-by-step explanation:

We have that:

f^2+g^4-2f+1 = a^2 + (g^2) ^2

And we want to find the value of a, so we should isolate it.

f^2 + g^4 - 2f + 1 = a^2 + g^ (2*2) = a^2 + g^4

where i used that (x^y) ^z = x^ (y*z)

We can remove the term g^4 in both sides of the equation and get:

f^2 - 2f + 1 = a^2

now we can apply the square rooth to both sides and get

√ (f^2 - 2f + 1) = a

So we just found the value of a.