Бізге берілген көпмүшелерді стандарт түрге келтірейік:

\(\displaystyle \quad \begin{array}{l}{\small 1)\,}2xyz^{\, 2}\cdot 3xz\cdot y-4xy^{\,2}z^{\,3}-yz^{\,3}\cdot y\cdot xy^{\,2}+xz^{\,2}\cdot xz-19xyz=\\\kern{3em} =(2\cdot 3)\cdot (x\cdot x\,)\cdot (\,y\cdot y\,)\cdot (z^{\, 2}\cdot z\,)-4xy^{\,2}z^{\,3}-x\cdot (\,y\cdot y\cdot y^{\,2})\cdot z^{\,3}+(x\cdot x\,) \cdot (z^{\,2}\cdot z\,)-\\\kern{33em} -19xyz=\\\kern{3em} =6\cdot x^{\,1+1}\cdot y^{\,1+1}\cdot z^{\,2+1}-4xy^{\,2}z^{\,3}-x\cdot y^{\,1+1+2}\cdot z^{\,3}+x^{\,1+1}\cdot z^{\,2+1}-19xyz=\\\kern{17em} =6x^{\,2}y^{\,2}z^{\,3}-4xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19xyz\,{\small ;}\end{array}\)

\(\displaystyle \quad \begin{array}{l}{\small 2)\,}-xz\cdot 5yz\cdot yz-6zy\cdot x^{\,2}y\cdot z^{\,2}+19xyz=\\\kern{5em} =-5\cdot x\cdot (\,y\cdot y\,)\cdot (z\cdot z\cdot z\,)-6\cdot x^{\,2}\cdot (\,y\cdot y\,)\cdot (z\cdot z^{\,2})+19xyz=\\\kern{5em} =-5\cdot x\cdot y^{\,1+1}\cdot z^{\,1+1+1}-6\cdot x^{\,2}\cdot y^{\,1+1}\cdot z^{\,1+2}+19xyz=\\\kern{19em} =-5xy^{\,2}z^{\,3}-6x^{\,2}y^{\,2}z^{\,3}+19xyz{\small .}\end{array}\)

Демек, бізге көпмүшелерді қосу керек

\(\displaystyle 6x^{\,2}y^{\,2}z^{\,3}-4xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19xyz\) және \(\displaystyle -5xy^{\,2}z^{\,3}-6x^{\,2}y^{\,2}z^{\,3}+19xyz{\small .}\)

Олардың қосындысын жазайық:

\(\displaystyle (\color{blue}{6x^{\,2}y^{\,2}z^{\,3}-4xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19xyz}\,)+(\color{green}{-5xy^{\,2}z^{\,3}-6x^{\,2}y^{\,2}z^{\,3}+19xyz}\,){\small .}\)

Жақшаларды ашайық:

\(\displaystyle \begin{array}{l}(6x^{\,2}y^{\,2}z^{\,3}-4xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19xyz\,)+(-5xy^{\,2}z^{\,3}-6x^{\,2}y^{\,2}z^{\,3}+19xyz\,)=\\\kern{5em} =6x^{\,2}y^{\,2}z^{\,3}-4xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19xyz-5xy^{\,2}z^{\,3}-6x^{\,2}y^{\,2}z^{\,3}+19xyz{\small .}\end{array}\)

Ұқсас мүшелерді келтірейік:

\(\displaystyle \begin{array}{l}6\color{blue}{x^{\,2}y^{\,2}z^{\,3}}-4\color{green}{xy^{\,2}z^{\,3}}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}-19\color{red}{xyz}-5\color{green}{xy^{\,2}z^{\,3}}-6\color{blue}{x^{\,2}y^{\,2}z^{\,3}}+19\color{red}{xyz}=\\\kern{2em} =(6\color{blue}{x^{\,2}y^{\,2}z^{\,3}}-6\color{blue}{x^{\,2}y^{\,2}z^{\,3}})+(-4\color{green}{xy^{\,2}z^{\,3}}-5\color{green}{xy^{\,2}z^{\,3}})-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}+(-19\color{red}{xyz}+19\color{red}{xyz}\,)=\\\kern{2em} =(6-6)\color{blue}{x^{\,2}y^{\,2}z^{\,3}}+(-4-5)\color{green}{xy^{\,2}z^{\,3}}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}+(-19+19)\color{red}{xyz}=\\\kern{6em} =0\cdot \color{blue}{x^{\,2}y^{\,2}z^{\,3}}-9\color{green}{xy^{\,2}z^{\,3}}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}+0\cdot \color{red}{xyz}=-9\color{green}{xy^{\,2}z^{\,3}}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}{\small .}\end{array}\)

Жауабы: \(\displaystyle -9xy^{\,2}z^{\,3}-xy^{\,4}z^{\,3}+x^{\,2}z^{\,3}{\small .}\)