Question

Bài 1:Phân tích các đa thức:

a)3x -3y+x²-y²

b)x²-4x²y²+y²+2xy

c)x³-3x²+3x-1-y³

d)x²-5x+6

e) x³ - 3x + 2

 

Answer 1

a) \(3x-3y+x^2-y^2\)

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

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

Answer 2

e) \(x^3-3x+2\)

\(=x^3-x-2x+2\)

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

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

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

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

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

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

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

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

Answer 3

d) \(x^2-5x+6\)

\(=x^2-2x-3x+6\)

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

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

Answer 4

\(b;x^2-4x^2y^2+y^2+2xy\)

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

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

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

Answer 5

c) \(x^3-3x^2+3x-1-y^3\)

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

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

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

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

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

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

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

Answer 6

\(c;x^3-3x^2+3x-1-y^3\)

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

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

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

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

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

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

# Kiểm tra rất kĩ từng bc r, bn có thể tham khảo ..........

Answer 7

Mơn mn ^^