Бізге берілген көпмүшелерді стандарт түрге келтірейік:

\(\displaystyle \quad \begin{array}{l}{\small 1)\,}4z^{\, 2}\cdot 7z\cdot z-5z^{\,3}-z^{\,2}\cdot 5\cdot z^{\,3}+z^{\,2}\cdot 10-119=\\\kern{4em} =(4\cdot 7)\cdot (z^{\, 2}\cdot z\cdot z\,)-5z^{\,3}-5\cdot (z^{\,2}\cdot z^{\,3})+10z^{\,2}-119=\\\kern{4em} =28\cdot z^{\, 2+1+1}-5z^{\,3}-5\cdot z^{\,2+3}+10z^{\,2}-119=\\\kern{7em} =28z^{\,4}-5z^{\,3}-5z^{\,5}+10z^{\,2}-119=-5z^{\,5}+28z^{\,4}-5z^{\,3}+10z^{\,2}-119{\small ;}\end{array}\)

\(\displaystyle \quad \begin{array}{l}{\small 2)\,}100-z\cdot10\cdot z-z^{\,4}\cdot 23\cdot z+19=\\\kern{5em} =100-10\cdot (z\cdot z\,) -23\cdot (z^{\,4}\cdot z\,)+19=100-10\cdot z^{\,1+1} -23\cdot z^{\,4+1}+19=\\\kern{5em} =100-10z^{\,2} -23z^{\,5}+19=(100+19)-10z^{\,2} -23z^{\,5}=\\\kern{17em} =119-10z^{\,2} -23z^{\,5}=-23z^{\,5}-10z^{\,2} +119{\small .}\end{array}\)

Демек, бізге көпмүшелерді қосу керек

\(\displaystyle -5z^{\,5}+28z^{\,4}-5z^{\,3}+10z^{\,2}-119\) және \(\displaystyle -23z^{\,5}-10z^{\,2} +119{\small .}\)

Олардың қосындысын жазайық:

\(\displaystyle (\color{blue}{-5z^{\,5}+28z^{\,4}-5z^{\,3}+10z^{\,2}-119})+(\color{green}{-23z^{\,5}-10z^{\,2} +119}){\small .}\)

Жақшаларды ашайық:

\(\displaystyle \begin{array}{l}(-5z^{\,5}+28z^{\,4}-5z^{\,3}+10z^{\,2}-119)+(-23z^{\,5}-10z^{\,2} +119)=\\\kern{13em} =-5z^{\,5}+28z^{\,4}-5z^{\,3}+10z^{\,2}-119-23z^{\,5}-10z^{\,2} +119{\small .}\end{array}\)

Нәтижелерін \(\displaystyle z\,{\small }\) дәрежелерінің кемуі бойынша жаза отырып, ұқсас мүшелерді келтірейік

\(\displaystyle \begin{array}{l}-5\color{blue}{z^{\,5}}+28z^{\,4}-5z^{\,3}+10\color{green}{z^{\,2}}-\color{red}{119}-23\color{blue}{z^{\,5}}-10\color{green}{z^{\,2}} +\color{red}{119}=\\\kern{9em} =(-5\color{blue}{z^{\,5}}-23\color{blue}{z^{\,5}})+28z^{\,4}-5z^{\,3}+(10\color{green}{z^{\,2}}-10\color{green}{z^{\,2}})+(-\color{red}{119}+\color{red}{119})=\\\kern{9em} =(-5-23)\color{blue}{z^{\,5}}+28z^{\,4}-5z^{\,3}+(10-10)\color{green}{z^{\,2}}+\color{red}{0}=\\\kern{15em} =-28\color{blue}{z^{\,5}}+28z^{\,4}-5z^{\,3}+0\cdot \color{green}{z^{\,2}}=-28\color{blue}{z^{\,5}}+28z^{\,4}-5z^{\,3}{\small .}\end{array}\)

Жауабы: \(\displaystyle -28z^{\,5}+28z^{\,4}-5z^{\,3}{\small .}\)