1:
a) \(4y\left(x-2\right)-5\left(2-x\right)\)
\(=4y\left(x-2\right)+5\left(x-2\right)\)
\(=\left(x-2\right)\left(4y+5\right)\)
b) \(x^2-4x+4-1\)
\(=\left(x-2\right)^2-1^2\)
\(=\left(x-2-1\right)\left(x-2+1\right)\)
\(=\left(x-3\right)\left(x-1\right)\)
c) \(5ay-3bx+ax-15by\)
\(=\left(5ay-15by\right)-\left(3bx-ax\right)\)
\(=5y\left(a-3b\right)-x\left(3b-a\right)\)
\(=5y\left(a-3b\right)+x\left(a-3b\right)\)
\(=\left(a-3b\right)\left(5y+x\right)\)
2:
a) \(x.\left(x-2\right)+x-2=0\)
\(\Rightarrow\left(x-2\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)
b) \(2\left(x+3\right)-x^2-3x=0\)
\(\Rightarrow2\left(x+3\right)-x\left(x+3\right)=0\)
\(\Rightarrow\left(x+3\right)\left(2-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\2-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}=-3\\x=2\end{matrix}\right.\)
