### Teorija

Polinoma reizināšana ar polinomu
"Lai sareizinātu polinomu ar polinomu, katru pirmā polinoma locekli reizina ar katru otrā polinoma locekli un iegūtos reizinājumus saskaita."
$\left(a+b\right)\cdot \left(c+d\right)=a\cdot c+a\cdot d+b\cdot c+b\cdot d=\mathit{ac}+\mathit{ad}+\mathit{bc}+\mathit{bd}$
"Reizinot pakāpes ar vienādām bāzēm, to kāpinātājus saskaita."
${a}^{m}\cdot {a}^{n}={a}^{m+n}$
Piemērs:
$\begin{array}{l}a\right)\phantom{\rule{0.294em}{0ex}}\left(7+b\right)\cdot \left(4{a}^{5}+2\mathit{ab}\right)=7\cdot 4{a}^{5}+7\cdot 2\mathit{ab}+b\cdot 4{a}^{5}+b\cdot 2\mathit{ab}=\\ \\ =28{a}^{5}+14\mathit{ab}+4{a}^{5}b+2a{b}^{2}\end{array}$

$\begin{array}{l}b\right)\phantom{\rule{0.294em}{0ex}}\left(5\mathit{xy}-3{x}^{2}\right)\cdot \left({x}^{2}+1\right)=5\mathit{xy}\cdot {x}^{2}+5\mathit{xy}\cdot 1-3{x}^{2}\cdot {x}^{2}-3{x}^{2}\cdot 1=\\ \\ =5{x}^{1+2}y+5\mathit{xy}-3{x}^{2+2}-3{x}^{2}=5{x}^{3}y+5\mathit{xy}-3{x}^{4}-3{x}^{2}\end{array}$
Svarīgi!
Uzmanīgi ar zīmēm!
$\begin{array}{l}c\right)\phantom{\rule{0.294em}{0ex}}\left(5{x}^{2}y-x\right)\cdot \left(2{x}^{2}-y\right)=5{x}^{2}y\cdot 2{x}^{2}+5{x}^{2}y\cdot \left(-y\right)-x\cdot 2{x}^{2}-x\cdot \left(-y\right)=\\ \\ =5\cdot 2{x}^{2+2}y-5{x}^{2}{y}^{1+1}-2{x}^{2+1}+\mathit{xy}=10{x}^{4}y-5{x}^{2}{y}^{2}-2{x}^{3}+\mathit{xy}\end{array}$

Atsauce:
Matemātika 7. klasei /Ilze France, Gunta Lāce, Ligita Pickaine, Anita Miķelsone - Lielvārde: Lielvārds, 2007. -141.lpp.