Multiply $$$\left(x - 1\right)^{2}$$$ using FOIL

Multiply $$$\left(x - 1\right)^{2} = \left(x - 1\right) \left(x - 1\right)$$$ using FOIL.

$$$\left({\color{red}\left(x\right)} + {\color{purple}\left(-1\right)}\right) \left({\color{green}\left(x\right)} + {\color{blue}\left(-1\right)}\right) = \underbrace{{\color{red}\left(x\right)} {\color{green}\left(x\right)}}_{\text{First}} + \underbrace{{\color{red}\left(x\right)} {\color{blue}\left(-1\right)}}_{\text{Outer}} + \underbrace{{\color{purple}\left(-1\right)} {\color{green}\left(x\right)}}_{\text{Inner}} + \underbrace{{\color{purple}\left(-1\right)} {\color{blue}\left(-1\right)}}_{\text{Last}} = x^{2} - x - x + 1 = x^{2} - 2 x + 1$$$

$$$\left(x - 1\right)^{2} = x^{2} - 2 x + 1$$$A