Confusion about binomial theorem

Question

Find the coefficient of $x^{22}$ in the expansion of $(1-3x)(1+x^3)^{10}$.

I know first the terms $x^{21}$ and $x^{22}$ will be calculate but the can't calculate the latter

Answer 1

From $$(1+x^3)^{10}$$ we have that

• there is one term: $ax^{21}=\binom{10}{3}x^{21}$;
• there is not any term for $x^{22}$ since $22$ is not a multiple of $3$.