Найдите сумму многочленов:
Раскроем скобки:
\(\displaystyle \begin{array}{l} (3xy^{\,2}z-2xyz^{\,2}+4xyz\,)+(3xyz^{\,2}+3xy^{\,2}z-xyz-11)=\\ \kern{16em} =3xy^{\,2}z-2xyz^{\,2}+4xyz+3xyz^{\,2}+3xy^{\,2}z-xyz-11 {\small .}\end{array}\)
Приведем подобные члены:
\(\displaystyle \begin{array}{l} 3\color{blue}{xy^{\,2}z}-2\color{green}{xyz^{\,2}}+4\color{red}{xyz}+3\color{green}{xyz^{\,2}}+3\color{blue}{xy^{\,2}z}-\color{red}{xyz}-11=\\ \kern{9em} =(3\color{blue}{xy^{\,2}z}+3\color{blue}{xy^{\,2}z}\,)+(-2\color{green}{xyz^{\,2}}+3\color{green}{xyz^{\,2}})+(4\color{red}{xyz}-\color{red}{xyz}\,)-11=\\ \kern{17em} =(3+3)\color{blue}{xy^{\,2}z}+(-2+3)\color{green}{xyz^{\,2}}+(4-1)\color{red}{xyz}-11=\\ \kern{26em} =6\color{blue}{xy^{\,2}z}+\color{green}{xyz^{\,2}}+3\color{red}{xyz}-11 {\small .}\end{array}\)
Ответ: \(\displaystyle 6xy^{\,2}z+xyz^{\,2}+3xyz-11{\small .}\)