Question

Phân tích đa thức thành nhân tử

a,\(4x^3y^2-8x^2y^3+12x^3y^4\)

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

c,\(\left(x+y\right)^2-2\left(x+y\right)\)

d,\(x\left(2-x\right)^2-\left(2-x\right)^3\)

hepl me Nguyễn Huy TúAkai HarumaT.Thùy NinhToshiro Kiyoshi

Answer 1

a, \(4x^3y^2-8x^2y^3+12x^3y^4\)

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

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

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

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

c, \(\left(x+y\right)^2-2\left(x+y\right)\)

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

d, \(x\left(2-x\right)^2-\left(2-x\right)^3\)

\(=\left(2-x\right)^2\left(x-2-x\right)=-2\left(x-2\right)^2\)

Answer 2

a, \(4x^3y^2-8x^2y^3+12x^3y^4\)

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

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

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

c, \(\left(x+y\right)^2-2\left(x+y\right)\)

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

d, \(x\left(2-x\right)^2-\left(2-x\right)^3\)

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

\(=2\left(x-2\right)^2\left(x-1\right)\)

Answer 3

a, \(4x^3y^2-8x^2y^3+12x^3y^4=4x^2y^2\left(x-2y+3xy^2\right)\)

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

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

d, \(x\left(2-x\right)^2-\left(2-x\right)^3=\left(2-x\right)^2\left[x-\left(2-x\right)\right]=\left(2x-2\right)\left(2-x\right)^2\)