Can a nonzero real number $a$ make both the coefficients of $x^2$ and $x^3$ vanish in \[(1+ax)

Question

Can a nonzero real number $a$ make both the coefficients of $x^2$ and $x^3$ vanish in $$(1+ax)^4(1-x)?$$ Prove your answer.

Accepted Answer

No; only $a=0$ makes both coefficients vanish.

Binomial Theorem