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

ô ri đúng 

TA CÓ: \(B-\left(x^2+xy+y^2\right)=2x^2-xy+y^2\)

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

\(B=2x^2-xy+y^2+x^2+xy+y^2\)

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

\(B=3x^2+2y^2\)

TA CÓ: \(\left(\frac{1}{2}.xy+x^2-\frac{1}{2}x^2y\right)-C=-xy+x^2y+1\)

\(\Rightarrow C=\left(\frac{1}{2}xy+x^2-\frac{1}{2}x^2y\right)-\left(-xy+x^2y+1\right)\)

\(C=\frac{1}{2}xy+x^2-\frac{1}{2}x^2y+xy-x^2y-1\)

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

\(C=\frac{3}{2}xy+\frac{-3}{2}x^2y+x^2-1\)

mk nha

Tìm đa thức B:

B - ( x² + xy + y² ) = 2x² - xy + y²

B = ( 2x² - xy + y² ) + ( x² + xy + y² )

B = ( 2x² + x² ) + ( - xy + xy ) + ( y² + y² )

B = 3x² + 2y²

Tìm đa thức C:

( \(\frac{1}{2}\). xy + x² - \(\frac{1}{2}\)x²y ) - C = - xy + x²y + 1

C = ( \(\frac{1}{2}\). xy + x² - \(\frac{1}{2}\)x²y ) - ( - xy + x²y + 1 )

C = \(\frac{1}{2}\). xy + x² - \(\frac{1}{2}\)x²y + xy - x²y + 1

C =(  \(\frac{1}{2}\)xy + xy ) + ( - \(\frac{1}{2}\)x²y - x²y ) + x² + 1

C = -1 ,5x²y + x² + 1

bài 1: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)

\(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)

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

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

Bài 2:

1: \(x^2y^2-8-1\)

\(=x^2y^2-9\)

\(=\left(xy-3\right)\left(xy+3\right)\)

2: \(x^3y-2x^2y+xy-xy^3\)

\(=xy\cdot x^2-xy\cdot2x+xy\cdot1-xy\cdot y^2\)

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

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

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

3: \(x^3-2x^2y+xy^2\)

\(=x\cdot x^2-x\cdot2xy+x\cdot y^2\)

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

4: \(x^2+2x-y^2+1\)

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

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

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

5: \(x^2+2x-4y^2+1\)

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

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

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

6: \(x^2-6x-y^2+9\)

\(=\left(x^2-6x+9\right)-y^2\)

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

b) Ta có: \(x^3-x^2y-xy^2+y^3\)

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

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

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

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