Verified Answer :

\(Use:\\distributive\ property:a(b+c)=ab+ac\\commutative\ property:a\cdot b=b\cdot a\\assiocative\ property:a\cdot(b\cdot c)=(a\cdot b)\cdot c\\and\ a^n\cdot a^m=a^{n+m}\\-----------------------\\\\4x(2x^2-7x+3)=(4x)(2x^2)+(4x)(-7x)+(4x)(3)\\\\=(4\cdot2)(x^1\cdot x^2)-(4\cdot7)(x^1\cdot x^1)+(4\cdot3)(x)\\\\=8x^{1+2}-28x^{1+1}+12x\\\\=\boxed{8x^3-28x^2+12x}\)

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