Жақшаларды көбейту үшін алдымен бірінші жақшаның әр мүшесін екінші жақшаға көбейтеміз:

\(\displaystyle \begin{array}{l}(\color{blue}{2x^{\,2}y^{\,3}}+\color{green}{3yz^{\,2}}\,)\cdot (3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4}\,)=\\\kern{11em} =\color{blue}{2x^{\,2}y^{\,3}}\cdot (3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4}\,)+\color{green}{3yz^{\,2}} \cdot (3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4}\,){\small .}\end{array}\)

Әрі қарай әр жақшаны олардың алдындағы көбейткішке көбейтіп, алынған бірмүшелерді стандарт түрге келтіреміз:

\(\displaystyle \begin{array}{l}\color{blue}{2x^{\,2}y^{\,3}}\cdot (3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4}\,)+\color{green}{3yz^{\,2}}\cdot (3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4}\,)=\\\kern{3em} =\color{blue}{2x^{\,2}y^{\,3}}\cdot 3x^{\,3}y^{\,2}z^{\,2}-\color{blue}{2x^{\,2}y^{\,3}}\cdot 4xz^{\,4}+(\color{green}{3yz^{\,2}}\cdot 3x^{\,3}y^{\,2}z^{\,2}-\color{green}{3yz^{\,2}}\cdot 4xz^{\,4}\,)=\\\kern{3em} =(2\cdot 3)\cdot (x^{\,2}\cdot x^{\,3})\cdot (\,y^{\,3}\cdot y^{\,2})\cdot z^{\,2}-(2\cdot 4)\cdot (x^{\,2}\cdot x\,)\cdot y^{\,3}\cdot z^{\,4}+\\\kern{13em} +((3\cdot 3)\cdot x^{\,3}\cdot (\,y\cdot y^{\,2})\cdot (z^{\,2}\cdot z^{\,2})-(3\cdot 4)\cdot x\cdot y\cdot (z^{\,2}\cdot z^{\,4}))=\\\kern{3em} =6\cdot x^{\,2+3}\cdot y^{\,3+2}\cdot z^{\,2}-8\cdot x^{\,2+1}\cdot y^{\,3}\cdot z^{\,4}+(9\cdot x^{\,3}\cdot y^{\,1+2}\cdot z^{\,2+2}-12\cdot x\cdot y\cdot z^{\,2+4})=\\\kern{19em} =6x^{\,5}y^{\,5}z^{\,2}-8x^{\,3}y^{\,3}z^{\,4}+(9x^{\,3}y^{\,3}z^{\,4}-12xyz^{\,6}){\small .}\end{array}\)

Жақшаларды ашайық:

\(\displaystyle \begin{aligned}6x^{\,5}y^{\,5}z^{\,2}-8x^{\,3}y^{\,3}z^{\,4}+(9x^{\,3}y^{\,3}z^{\,4}-12xyz^{\,6})=6x^{\,5}y^{\,5}z^{\,2}-8x^{\,3}y^{\,3}z^{\,4}+9x^{\,3}y^{\,3}z^{\,4}-12xyz^{\,6}{\small .}\end{aligned}\)

Алынған көпмүшені ұқсас бірмүшелерді келтіре отырып, стандарт түрге келтірейік:

\(\displaystyle \begin{aligned}6x^{\,5}y^{\,5}z^{\,2}-8\color{blue}{x^{\,3}y^{\,3}z^{\,4}}+9\color{blue}{x^{\,3}y^{\,3}z^{\,4}}-12xyz^{\,6}&=6x^{\,5}y^{\,5}z^{\,2}+(-8\color{blue}{x^{\,3}y^{\,3}z^{\,4}}+9\color{blue}{x^{\,3}y^{\,3}z^{\,4}})-12xyz^{\,6}=\\&=6x^{\,5}y^{\,5}z^{\,2}+(-8+9)\color{blue}{x^{\,3}y^{\,3}z^{\,4}}-12xyz^{\,6}=\\&=6x^{\,5}y^{\,5}z^{\,2}+\color{blue}{x^{\,3}y^{\,3}z^{\,4}}-12xyz^{\,6}{\small .}\end{aligned}\)

Осылайша,

\(\displaystyle (2x^{\,2}y^{\,3}+3yz^{\,2})(3x^{\,3}y^{\,2}z^{\,2}-4xz^{\,4})=6x^{\,5}y^{\,5}z^{\,2}+x^{\,3}y^{\,3}z^{\,4}-12xyz^{\,6}{\small .}\)

Жауабы: \(\displaystyle 6x^{\,5}y^{\,5}z^{\,2}+x^{\,3}y^{\,3}z^{\,4}-12xyz^{\,6}{\small .}\)