Question

Phân tích đa thức sau thành nhân tử:

a) x(x - y) + x - y

b) 2x + 2y - x(x + y)

c) 5x² - 5xy - 10x + 10y

d) 4x² + 8xy - 3x - 6y

e) 2x² + 2y² - x²z + z - y²z - 2

Answer 1

a) \(x\left(x-y\right)+x-y\)

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

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

b) \(2x+2y-x\left(x+y\right)\)

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

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

c) \(5x^2-5xy-10x+10y\)

\(=5x\left(x-y\right)-10\left(x-y\right)\)

\(=\left(x-y\right)\left(5x-10\right)\)

d) \(4x^2+8xy-3x-6y\)

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

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

e) \(2x^2+2y^2-x^2z+z-y^2z-2\)

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

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

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