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(r3s+t)(2rs+t)(r-3 s+t)(2 r-s+t)


Answered 1 year ago
Answered 1 year ago
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In determining the product of polynomials with 33 or more terms, use the vertical multiplication method.

ddssdsr3s+1t2r2s+1trt3st+t2      t(r3s+t)1rs+3s2+3kn2stt2   s(r3s+t)2r26rs3n2+2rt3stk2    2r(r3s+t)2r27rs+3s2+3rt4st+t2Add in columns. \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 2r27rs+3s2+3rt4st+t22r^2-7rs+3s^2+3rt-4st+t^2

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