# Determine the product of the polynomials.4x^2(3x^3+2x^2-5x+1)

Determine the product of the polynomials.
$$\displaystyle{4}{x}^{{2}}{\left({3}{x}^{{3}}+{2}{x}^{{2}}-{5}{x}+{1}\right)}$$

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nitruraviX
Expand the polynomials as, $$\displaystyle{4}{x}^{{2}}{\left({3}{x}^{{3}}+{2}{x}^{{2}}-{5}{x}+{1}\right)}$$
$$\displaystyle={4}{x}^{{2}}\times{3}{x}^{{3}}+{4}{x}^{{2}}\times{2}{x}^{{2}}+{4}{x}^{{2}}\times{\left(-{5}{x}\right)}+{4}{x}^{{2}}\times{1}$$
$$\displaystyle={12}{x}^{{{2}+{3}}}+{8}{x}^{{{2}+{2}}}-{20}{x}^{{{2}+{1}}}+{4}{x}^{{2}}$$
$$\displaystyle={12}{x}^{{5}}+{8}{x}^{{4}}-{20}{x}^{{3}}+{4}{x}^{{2}}$$