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(4x^3-x^2+2x) (3x^3+x^2+4x)=
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use foil!
\[12x^6+x^5+21x^4-2x^3+8x^2\]
I would probably just distribute the second trinomial to each term in the first 4x^3 (3x^3 + x^2 + 4x) - x^2 (3x^3 + x^2 + 4x) + 2x(3x^3 + x^2 + 4x) and then distribute each single term through and simplify by adding like terms
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