Multiply the following polynomials .
$(m^{3} + 2 m + 3) (m^{3} - 2 m^{2} + 3 m + 2)$

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Solution

$(m^{3} + 2 m + 3) (m^{3} - 2 m^{2} + 3 m + 2)$
$= m^{3} (m^{3} - 2 m^{2} + 3 m + 2) + 2 m (m^{3} - 2 m^{2} + 3 m + 2) + 3 (m^{3} - 2 m^{2} + 3 m + 2)$
$= m^{6} - 2 m^{5} + 3 m^{4} + 2 m^{2} + 2 m^{4} - 4 m^{3} + 6 m^{2} + 4 m + 3 m^{3} - 6 m^{2} + 9 m + 6$
$= m^{6} - 2 m^{5} + 5 m^{4} - m^{3} + 2 m^{2} + 13 m + 6$

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