Coefficient of x^8 in quartic expansion

Find the coefficient of $x^{8}$ in the expansion of $(1 - 2 x + 3 x^{2} - 4 x^{3})^{4}$ .

~8 minAnswer checked instantlyMultinomial theoremSeries expansion

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XV. Multinomial Theorem, Examples XV, No. 8

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).