Question

phân tích đa thức thành nhân tử :

a) \(2x^2+2xy^2-x-y\)

b) \(8x^3-12x^2+6x-1\)

c) \(4x^2-4xy+y^2-9\)

d)\(27x^3-y^3+3y^2-3y+1\)

e) \(25x^4-10x^2y+y^2\)

f) \(x^2-2x-4y^2-4y\)

g) \(x^4+2x-4x-4\)

h) \(x^2-7xy+10y^2\)

Answer 1

*Trả lời:

a) Có vẻ như đề sai nên mình sửa lại:

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

b) \(8x^3-12x^2+6x-1=\left(2x\right)^3-3\cdot4x^2+3.2x-1=\left(2x-1\right)^3\)

c)\(4x^2-4xy+y^2-9=\left(4x^2-4xy+y^2\right)-9=\left(2x-y\right)^2-3^2=\left(2x-y-3\right)\left(2x-y+3\right)\)

e)\(25x^4-10x^2y+y^2=\left(5x^2\right)^2-2.5x^2y+y^2=\left(5x^2-y\right)^2\)

h)\(x^2-7xy+10y^2=x^2-2xy-5xy+10y^2=\left(x^2-2xy\right)-\left(5xy-10y^2\right)=x\left(x-2y\right)-5y\left(x-2y\right)=\left(x-5y\right)\left(x-2y\right)\)