number of terms in the expansion containing powers of $x$ 
How do i find the number of terms containing powers of $x$ in the expansion of: $$(1+x)^{100}(1+x^2-x)^{101}$$

I tried using $(1+x)((1+x(1+(x)^2-x))^{100})$ which simplified into : $$(1+x)(1+x^3)^{100}$$
but i'm not sure if this is the correct approach and also what do i do to simplify it further to get the answer?
It's a multiple choice question with options A:202, B:302, C:301 and D:101
please explain the method to solve questions of this type :)

Alternatively:
$$\begin{align}(1+x)^{100}(1+x^2-x)^{101}&=(1+x)^{100}\cdot \left(\frac{(1+x)(x^2-x+1)}{1+x}\right)^{101}=\\
&=(1+x)^{100}\cdot \frac{(x^3+1)^{101}}{(1+x)^{101}}=\\
&=\frac{(x^3+1)(x^3+1)^{100}}{1+x}=\\
&=(x^2-x+1)(x^3+1)^{100}=\\
&=x^{302}-x^{301}+x^{300}+100x^{299}-100x^{298}+100x^{297}+\cdots +x^2-x+1.\end{align}$$
Hence, there are $302$ terms with $x$.
