Question

phân tích các đa thức sau thành nhân tử :

a)(x-5)2 + ( x+5).(x-5) - ( 5-x).(2x+1)

b) (3x-2).(4x-3) - ( 2-3x).(x-1)-2.(3x - 2).( x+1)

c)(a-b).( a+2b) - ( b-a). (2a-b) - (a-b).(a+3b)

d)5xy³ - 2xyz - 15y² + 6z

e)ab³c² -a²b²c² + ab²c³- a²bc³

f) x²( y-z) + y²(z-x) + z² (x- y)

Answer 1

a) \(=\left(x-5\right)\left(2+x+5-2x-1\right)=\left(x-5\right)\left(6-x\right)\)

Answer 2

b) \(=\left(3x-2\right)\left(4x-3-x+1-x-1\right)=\left(3x-2\right)\left(3x-3\right)=3\left(x-1\right)\left(3x-2\right)\)

Answer 3

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

Answer 4

d) \(=\left(5xy^3-15y^2\right)+\left(-2xyz+6z\right)=5xy^2\left(xy-3\right)-2x\left(xy-3\right)=\left(xy-3\right)\left(5xy^2-2x\right)\)

Answer 5

e) \(=\left(ab^3c^2-a^2b^2c^2\right)+\left(ab^2c^3-a^2bc^3\right)=ab^2c^2\left(b-a\right)+abc^3\left(b-a\right)=abc^2\left(b-a\right)\left(b+c\right)\)