Câu 1:
1:
a: \(x^2-3xy=x\cdot x-x\cdot3y=x\left(x-3y\right)\)
b: \(y^2+8y+16-4x^2\)
\(=\left(y+4\right)^2-\left(2x\right)^2\)
=(y+4-2x)(y+4+2x)
2:
a: \(\left(x-1\right)^2-x\left(x-3\right)=2\)
=>\(x^2-2x+1-x^2+3x=2\)
=>x+1=2
=>x=2-1
=>x=1
b: \(2x\left(x+1\right)-x-1=0\)
=>2x(x+1)-(x+1)=0
=>(x+1)(2x-1)=0
=>\(\left[\begin{array}{l}x+1=0\\ 2x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-1\\ x=\frac12\end{array}\right.\)
Câu 2:
1: \(A=\left(2x+3\right)\left(2x-1\right)-\left(2x+1\right)^2\)
\(=4x^2-2x+6x-3-\left(4x^2+4x+1\right)\)
\(=4x^2+4x-3-4x^2-4x-1=-4\)
=>A là hằng số
2:
\(\left(2x^3-3x^2+7x-3\right)=\left(2x-1\right)\cdot P\left(x\right)\)
=>\(P\left(x\right)\cdot\left(2x-1\right)=2x^3-x^2-2x^2+x+6x-3=\left(2x-1\right)\left(x^2-x+3\right)\)
=>\(P\left(x\right)=x^2-x+3\)
