Question

Phân tích các đa thức sau thành nhân tử

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

b) \(4x^2-4xy-6y^2+6xy\)

c) \(18x^5y+18x^3y-2x^3y^5-2xy^5\)

d) \(-12x^5-12x^3y-3xy^2+36x^4+36x^2y+9y^2\)

Answer 1

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

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

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

c) \(18x^5y+18x^3y-2x^3y^5-2xy^5=18x^3y\left(x^2+1\right)-2xy^5\left(x^2+1\right)\)

\(=\left(x^2+1\right)\left(18x^3y-2xy^5\right)=2xy\left(x^2+1\right)\left(9x^2-y^4\right)=2xy\left(x^2+1\right)\left(3x-y^2\right)\left(3x+y^2\right)\)

d)

Answer 2

d) \(-12x^5-12x^3y-3xy^2+36x^4+36x^2y+9y^2=-3x\left(4x^4+4x^2y+y^2\right)+9y\left(4x^4+4x^2y+y^2\right)\)\(=\left(4x^4+4x^2y+y^2\right)\left(9-3x\right)\)