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Теориясы: Көпмүшелерді қосу және азайту

Тапсырма

Көпмүшелердің қосындысын табыңыз:

 

\(\displaystyle (3xy^{\,2}z-2xyz^{\,2}+4xyz)+(3xyz^{\,2}+3xy^{\,2}z-xyz-11)=\)
6xy^2z+xyz^2+3xyz-11
Шешім

Жақшаларды ашайық:

\(\displaystyle \begin{array}{l}(3xy^{\,2}z-2xyz^{\,2}+4xyz\,)+(3xyz^{\,2}+3xy^{\,2}z-xyz-11)=\\\kern{16em} =3xy^{\,2}z-2xyz^{\,2}+4xyz+3xyz^{\,2}+3xy^{\,2}z-xyz-11{\small .}\end{array}\)

 

Ұқсас мүшелерді келтірейік:

\(\displaystyle \begin{array}{l}3\color{blue}{xy^{\,2}z}-2\color{green}{xyz^{\,2}}+4\color{red}{xyz}+3\color{green}{xyz^{\,2}}+3\color{blue}{xy^{\,2}z}-\color{red}{xyz}-11=\\\kern{9em} =(3\color{blue}{xy^{\,2}z}+3\color{blue}{xy^{\,2}z}\,)+(-2\color{green}{xyz^{\,2}}+3\color{green}{xyz^{\,2}})+(4\color{red}{xyz}-\color{red}{xyz}\,)-11=\\\kern{17em} =(3+3)\color{blue}{xy^{\,2}z}+(-2+3)\color{green}{xyz^{\,2}}+(4-1)\color{red}{xyz}-11=\\\kern{26em} =6\color{blue}{xy^{\,2}z}+\color{green}{xyz^{\,2}}+3\color{red}{xyz}-11{\small .}\end{array}\)


Жауабы: \(\displaystyle 6xy^{\,2}z+xyz^{\,2}+3xyz-11{\small .}\)