Svarīgi!
${\left(a-b\right)\left(a-b\right)=\left(a-b\right)}^{2}={a}^{2}-2\mathit{ab}+{b}^{2}$

Divu skaitļu starpības kvadrāts vienāds ar pirmā skaitļa kvadrātu mīnus divkāršots abu skaitļu reizinājums, plus otrā skaitļa kvadrāts.
Formulas pierādījums:

$\begin{array}{l}{\left(a-b\right)}^{2}=\left(a-b\right)\cdot \left(a-b\right)=\\ =a\cdot a+a\cdot \left(-b\right)-b\cdot a-b\cdot \left(-b\right)=\\ ={a}^{2}-\underset{¯}{\mathit{ab}}-\underset{¯}{\mathit{ba}}+{b}^{2}=\\ ={a}^{2}-2\mathit{ab}+{b}^{2}\end{array}$

Lai veiktu šo reizināšanu, var izmantot formulu, bet vari reizināt arī kā binomu ar binomu (iekavu ar iekavu).
Piemērs:
Formulas pielietojums:
${\left(a-b\right)}^{2}={a}^{2}-2\mathit{ab}+{b}^{2}$

1)
$\begin{array}{l}{\left(x-1\right)}^{2}={x}^{2}-2\cdot x\cdot 1+{1}^{2}=\\ ={x}^{2}-2x+1\end{array}$

2)
$\begin{array}{l}{\left(2x-y\right)}^{2}={\left(2x\right)}^{2}-2\cdot 2x\cdot y+{y}^{2}=\\ =4{x}^{2}-4\mathit{xy}+{y}^{2}\end{array}$

3)
$\begin{array}{l}{\left(3m-5\right)}^{2}={\left(3m\right)}^{2}-2\cdot 3m\cdot 5+{5}^{2}=\\ ={9m}^{2}-30m+25\end{array}$

Iekavu atvēršana bez formulām (reizinot kā polinomus - pirmo iekavu ar otro iekavu)

1)
$\begin{array}{l}{\left(x-5\right)}^{2}=\left(x-5\right)\cdot \left(x-5\right)=\\ =x\cdot x+x\cdot \left(-5\right)-5\cdot x-5\cdot \left(-5\right)=\\ ={x}^{2}-5x-5x+25={x}^{2}-10x+25\end{array}$

2)
$\begin{array}{l}{\left(2x-1\right)}^{2}=\left(2x-1\right)\cdot \left(2x-1\right)=\\ =2x\cdot 2x+2x\cdot \left(-1\right)-1\cdot 2x-1\cdot \left(-1\right)=\\ ={4x}^{2}-2x-2x+1=\\ =4{x}^{2}-4x+1\end{array}$

3)
$\begin{array}{l}{\left(6z-5\right)}^{2}=\left(6z-5\right)\cdot \left(6z-5\right)=\\ =6z\cdot 6z+6z\cdot \left(-5\right)-5\cdot 6z-5\cdot \left(-5\right)=\\ =36{z}^{2}-30z-30z+25=\\ =36{z}^{2}-60z+25\end{array}$