Question

Phân tích đa thức thành nhân tử:

a) \(25x^2y^4-4x^4y^2\)

b) \(x^2-5x+2xy-10y\)

c) \(4x^2+4x-9y^2+6y\)

Answer 1

a: \(25x^2y^4-4x^4y^2\)

\(=25x^2y^2\cdot y^2-4x^2y^2\cdot x^2\)

\(=x^2y^2\left(25y^2-4x^2\right)\)

\(=x^2y^2\left(5y-2x\right)\left(5y+2x\right)\)

b: 

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

\(=x\left(x-5\right)+2y\left(x-5\right)\)

=(x-5)(x+2y)

c: \(4x^2+4x-9y^2+6y\)

\(=\left(4x^2-9y^2\right)+\left(4x+6y\right)\)

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

=(2x+3y)(2x-3y+2) 

Answer 2

a: \(25x^2y^4-4x^4y^2\)

\(=25x^2y^2\cdot y^2-4x^2y^2\cdot x^2\)

\(=x^2y^2\left(25y^2-4x^2\right)\)

\(=x^2y^2\left(5y-2x\right)\left(5y+2x\right)\)

b: 

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

\(=x\left(x-5\right)+2y\left(x-5\right)\)

=(x-5)(x+2y)

c: \(4x^2+4x-9y^2+6y\)

\(=\left(4x^2-9y^2\right)+\left(4x+6y\right)\)

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

=(2x+3y)(2x-3y+2)