Question

Multiply the following polynomials.

(i) (m³ $-$2m + 3)(m⁴$-$2m² + 3m + 2)

(ii) (5m³ $-$2)(m² $-$ m + 3)

Answer 1

(i)
$$\begin{gathered} \left(m^3-2m+3\right)\left(m^4-2m^2+3m+2\right) \\ =m^3\left(m^4-2m^2+3m+2\right)-2m\left(m^4-2m^2+3m+2\right)+3\left(m^4-2m^2+3m+2\right) \\ =m^7-2m^5+3m^4+2m^3-2m^5+4m^3-6m^2-4m+3m^4-6m^2+9m+6 \\ =m^7-2m^5-2m^5+3m^4+3m^4+2m^3+4m^3-6m^2-6m^2-4m+9m+6 \\ =m^7-4m^5+6m^4+6m^3-12m^2+5m+6 \end{gathered}$$
(ii)
$$\begin{gathered} \left(5m^3-2\right)\left(m^2-m+3\right) \\ =5m^3\left(m^2-m+3\right)-2\left(m^2-m+3\right) \\ =5m^5-5m^4+15m^3-2m^2+2m-6 \end{gathered}$$