Bài 6:
a: \(\left(a-b\right)\cdot x+\left(b-a\right)\cdot y-b+a\)
\(=\left(a-b\right)\cdot x-y\left(a-b\right)+\left(a-b\right)\)
\(=\left(a-b\right)\left(x-y+1\right)\)
b: \(\left(a+b-c\right)\cdot x^2-x\left(c-a-b\right)\)
\(=\left(a+b-c\right)\cdot x^2+x\left(a+b-c\right)\)
\(=x\left(a+b-c\right)\left(x+1\right)\)
Bài 5:
a: \(x^3-\dfrac{1}{4}x=0\)
=>\(x\left(x^2-\dfrac{1}{4}\right)=0\)
=>\(x\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-\dfrac{1}{2}=0\\x+\dfrac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
b: \(\left(2x-1\right)^2-\left(x+3\right)^2=0\)
=>\(\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\)
=>(x-4)(3x+2)=0
=>\(\left[{}\begin{matrix}x-4=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\\x=4\end{matrix}\right.\)
c: \(x^2-3x=0\)
=>\(x\cdot x-x\cdot3=0\)
=>\(x\left(x-3\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
d: \(\left(x-2\right)\left(2x+1\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\2x+1=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=2\\x=-\dfrac{1}{2}\end{matrix}\right.\)
e: \(x^2+4x+4=0\)
=>\(x^2+2\cdot x\cdot2+2^2=0\)
=>\(\left(x+2\right)^2=0\)
=>x+2=0
=>x=-2
f: \(x^2-3x+2=0\)
=>\(x^2-x-2x+2=0\)
=>\(x\left(x-1\right)-2\left(x-1\right)=0\)
=>(x-1)(x-2)=0
=>\(\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)
