#### Answer

$8x^{4}-28x^{3}+4x^{2}$

#### Work Step by Step

We start with the given expression: $4x(2x^3-7x^2+x)$
We apply the distributive property to multiply the monomial by the binomial: $(4x)(2x^3)+(4x)(-7x^2)+(4x)(x)$
We multiply the coefficients and add the exponents on each term to arrive at our answer: $$8x^{3+1}-28x^{1+2}+4x^{1+1}$$$$8x^{4}-28x^{3}+4x^{2}$$