a) \(3x-3y+x^2-y^2\)
\(=3\left(x-y\right)+\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\left(3+x+y\right)\)
e) \(x^3-3x+2\)
\(=x^3-x-2x+2\)
\(=x\left(x^2-1\right)-2\left(x-1\right)\)
\(=x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left[x\left(x+1\right)-2\right]\)
\(=\left(x-1\right)\left(x^2+x-2\right)\)
\(=\left(x-1\right)\left(x^2-x+2x-2\right)\)
\(=\left(x-1\right)\left[x\left(x-1\right)+2\left(x-1\right)\right]\)
\(=\left(x-1\right)\left(x-1\right)\left(x+2\right)\)
\(=\left(x-1\right)^2\left(x+2\right)\)
d) \(x^2-5x+6\)
\(=x^2-2x-3x+6\)
\(=x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\)
\(b;x^2-4x^2y^2+y^2+2xy\)
\(=\left(x^2+2xy+y^2\right)-4x^2y^2\)
\(=\left(x+y\right)^2-\left(2xy\right)^2\)
\(=\left(x+y-2xy\right)\left(x+y+2xy\right)\)
c) \(x^3-3x^2+3x-1-y^3\)
\(=\left(x^3-1\right)-\left(3x^2-3x\right)-y^3\)
\(=\left(x-1\right)\left(x^2+x+1\right)-3x\left(x-1\right)-y^3\)
\(=\left(x-1\right)\left(x^2+x+1-3x\right)-y^3\)
\(=\left(x-1\right)\left(x^2-2x+1\right)-y^3\)
\(=\left(x-1\right)\left(x-1\right)^2-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(c;x^3-3x^2+3x-1-y^3\)
\(=\left[\left(x-1\right)\left(x^2+x+1\right)-3x\left(x-1\right)\right]-y^3\)
\(=\left[\left(x-1\right)\left(x^2+x+1-3x\right)\right]-y^3\)
\(=\left[\left(x-1\right)\left(x^2-2x+1\right)\right]-y^3\)
\(=\left[\left(x-1\right)\left(x-1\right)^2\right]-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
# Kiểm tra rất kĩ từng bc r, bn có thể tham khảo ..........