1) \(2\left(x-1\right)^3-\left(x-1\right)=\left(x-1\right)\left(2\left(x-1\right)^2-1\right)\)

2) \(y\left(x-2y\right)^2+xy^2\left(2y-x\right)=\left(2y-x\right)\left(2\left(2y-x\right)+1\right)=\left(2y-x\right)\left(4y-2x+1\right)\)

3) \(xy\left(x+y\right)-x-y=xy\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(xy-1\right)\) (xem lại đề sửa -2x thành -x mới đúng)

4) \(xy\left(x-3y\right)-2x+6y=xy\left(x-3y\right)-2\left(x-3y\right)=\left(x-3y\right)\left(xy-2\right)\)

a, \(\frac{x^2}{x+1}+\frac{2x}{x^2-1}+\frac{1}{x+1}+1\)

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

\(=\frac{x^3-x^2-2x+x-1-x^2-1}{\left(x-1\right)\left(x+1\right)}\)

\(=\frac{x^3-2x^2-x-2}{\left(x-1\right)\left(x+1\right)}\)

a: \(x\left(2x-y\right)-y\left(2x-y\right)=\left(2x-y\right)\left(x-y\right)\)

c: \(x^2-3x+3y-y^2\)

\(=\left(x-y\right)\left(x+y\right)-3\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-3\right)\)

b: \(x^2-6x-7=\left(x-7\right)\left(x+1\right)\)

a) \(x\left(2x-y\right)-y\left(2x-y\right)=\left(2x-y\right)\left(x-y\right)\)

b) \(x^2-6x-7=x\left(x-7\right)+\left(x-7\right)=\left(x-7\right)\left(x+1\right)\)

c) \(x^2-3x+3y-y^2=\left(x-y\right)\left(x+y\right)-3\left(x-y\right)=\left(x-y\right)\left(x+y-3\right)\)

d) \(x^3-xy+2y-8=\left(x-2\right)\left(x^2+2x+4\right)-y\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2+2x+4-y\right)\)

Bài 2: 

a: \(3x^2-3xy=3x\left(x-y\right)\)

b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)

c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)

d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)

ỳtct7ct7c7c7t79tc9

a) \(\dfrac{x^2}{x+1}+\dfrac{2x}{x^2-1}+\dfrac{1}{1+x+1}\) \(=\dfrac{x^2.\left(x-1\right)\left(x+2\right)}{\left(x+1\right).\left(x-1\right)\left(x+2\right)}+\dfrac{2x.\left(x+2\right)}{\left(x-1\right).\left(x+1\right).\left(x+2\right)}+\dfrac{\left(x-1\right).\left(x+1\right)}{\left(x-1\right)\left(x+1\right).\left(x+2\right)}\)

\(=\dfrac{x^2.\left(x-1\right).\left(x+2\right)+2x.\left(x+2\right)+\left(x-1\right)\left(x+1\right)}{\left(x+1\right).\left(x-1\right).\left(x+2\right)}\)

\(=\dfrac{x^4+x^3-2x^2+2x^2+4x+x^2-1}{\left(x-1\right)\left(x+1\right).\left(x+2\right)}\)

\(=\dfrac{x^4+x^3+x^2+4x-1}{\left(x^2-1\right).\left(x+2\right)}\)

\(=\dfrac{x^4+x^3+x^2+4x-1}{x^3+2x^2-x-2}\)

a, \(\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}=\frac{x}{y\left(x-y\right)}+\frac{2x-y}{x\left(y-x\right)}\)

\(=\frac{x^2}{xy\left(x-y\right)}-\frac{2xy-y^2}{xy\left(x-y\right)}=\frac{\left(x-y\right)^2}{xy\left(x-y\right)}=\frac{x-y}{xy}\)

b, \(\frac{1}{x+1}+\frac{1}{x-1}+\frac{2x^2}{x^2-1}=\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2x^2}{\left(x-1\right)\left(x+1\right)}\)

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

a: \(a^2+6ab+9b^2-1\)

\(=\left(a+3b\right)^2-1^2\)

\(=\left(a+3b+1\right)\left(a+3b-1\right)\)

b: \(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)

\(=\left(2x-5\right)\left(2x+5\right)-\left(2x+7\right)\left(2x-5\right)\)

\(=\left(2x-5\right)\left(2x+5-2x-7\right)\)

\(=-2\left(2x-5\right)\)

c: \(5\left(x+3y\right)-15x\left(x+3y\right)\)

\(=\left(x+3y\right)\left(-15x+5\right)\)

\(=-5\left(3x-1\right)\left(x+3y\right)\)

d: \(x\left(x+y\right)^2-y\left(x+y\right)^2+xy-x^2\)

\(=\left(x+y\right)^2\cdot\left(x-y\right)-x\left(x-y\right)\)

\(=\left(x-y\right)\left[\left(x+y\right)^2-x\right]\)

e: \(a^2-6a+9-b^2\)

\(=\left(a-3\right)^2-b^2\)

\(=\left(a-3-b\right)\left(a-3+b\right)\)

f: \(x^3-y^3-3x^2+3x-1\)

\(=\left(x^3-3x^2+3x-1\right)-y^3\)

\(=\left(x-1\right)^3-y^3\)

\(=\left(x-1-y\right)\left[\left(x-1\right)^2+y\left(x-1\right)+y^2\right]\)

Biến đổi mỗi đa thức theo hướng làm xuất hiện thừa số x+y-2 \(M=x^3+x^2y-2x^2-xy-y^2+3y+x-1\)

\(M=x^3+x^2y-2x^2-xy-y^2+\left(2y+y\right)+x-\left(-2+1\right)\)

\(M=\left(x^3+x^2y-2x^2\right)-\left(xy+y^2-2y\right)+\left(x+y-2\right)+1\)

\(M=\left(x^2.x+x^2.y-2x^2\right)-\left(x.y+y.y-2y\right)+\left(x+y-2\right)+1\)

\(M=x^2.\left(x+y-2\right)-y.\left(x+y-2\right)+\left(x+y-2\right)+1\)

\(M=x^2.0+y.0+0+1\)

\(M=1\)

\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-2\)

\(N=x^3+x^2y-2x^2-xy^2+x^2y+2xy+2y+2x-\left(-4+2\right)\)

\(N=\left(x^3+x^2y-2x^2\right)-\left(x^2y+xy^2-2xy\right)+\left(2x+2y-4\right)+2\)

\(N=\left(x^2x+x^2y-2x^2\right)-\left(xyx+xyy-2xy\right)+\left(2x+2y-4\right)+2\)

\(N=x^2\left(x+y-2\right)-xy\left(x+y-2\right)+2\left(x+y-2\right)+2\)

\(N=x^2.0-xy.0+2.0+2\)

\(N=2\)

\(P=x^4+2x^3y-2x^3+x^2y^2-2x^2y-x\left(x+y\right)+2x+3\)

\(P=\left(x^4+x^3y-2x^3\right)+\left(x^3y+x^2y^2-2x^2y\right)-\left(x^2+xy-2x\right)+3\)\(P=\left(x^3x+x^3y-2x^3\right)+\left(x^2y.x+x^2yy-2x^2y\right)-\left(xx+xy-2x\right)+3\)

\(P=x^3\left(x+y-2\right)+x^2y\left(x+y-2\right)-x\left(x+y-2\right)+3\)

\(P=x^3.0+x^2y.0-x.0+3\)

\(P=3\)

Tích mình nha!

Mà bài này hình như học ở lớp 7 rồi!