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# Find each product. See the examples in this section.$(r-3 s+t)(2 r-s+t)$

Solution

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In determining the product of polynomials with $3$ or more terms, use the vertical multiplication method.

$\begin{array}{r} \phantom{ddssds}r -3s + \phantom1t\\ 2r -\phantom2s + \phantom1t\\ \overline{rt-3st+t^2} & \leftarrow\space\ \ \ \ \ {t}(r-3s+t)\\ -\phantom1rs+3s^2\phantom{+3kn}-\phantom2st\phantom{-t^2}& \leftarrow\ \ \ {-s}(r-3s+t)\\ 2r^2-6rs\phantom{-3n^2}+2rt\phantom{-3st-k^2}& \leftarrow\ \ \ \ 2r(r-3s+t)\\ \overline{2r^2-7rs+3s^2+3rt-4st+t^2} &\quad \quad\text{Add in columns. } \end{array}$

The product of the polynomials is $2r^2-7rs+3s^2+3rt-4st+t^2$

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