# Consider $R=k[x_1,x_2,…x_n]$. Difference between $(f_1,..,f_k)$ and $k[f_1,…f_k]$

I'm confused on the difference between these two objects. My book says that we can see the difference when considering the simple case where $$f_1=x^2\in k[x]$$, and see that $$1\in k[x^2]$$, but $$1\notin (x^2)$$.

However I couldn't figure out why $$1\in k[x^2]$$. Could anyone help illustrate this?

$$k[x^2]$$ denotes the set of polynomials in $$x^2$$ with coefficients in the field $$k$$, i.e. the set of (ordinary) polynomials with only monomials of even degree (+0). $$1$$ has degree $$0$$, as all non-zero constants, and if I remember well, $$0$$ is even. So $$1$$ belongs to $$k[x^2]$$.