Đặt a - 2b + c = x 

b - 2c + a = y

c - 2a + b = z

Ta có x + y + z = 0

=> x + y = - z

=> (x + y)³ = (-z)³

=> x³ + y³ + 3xy(x + y) = - z³ 

=> x³ + y³ + z³ = -3xy(x + y) 

=> x³ + y³ + z³ = 3xyz

mà x³ + y³ + z³ = 0 

=> 3xyz = 0 

=> xyz = 0

=> x = 0 hoặc y = 0 hoặc z = 0

Khi x = 0 => a - 2b + c = 0 

=> a + c = 2b

=> a + b + c = 3b \(⋮\)3

Khi y = 0 => b - 2c + a = 0

=> a + b = 2c 

=> a + b + c = 3c \(⋮\)3

Khi z = 0 => c - 2a + b = 0

=> b + c = 2a

=> a + b + c = 3a \(⋮\)3

Vậy a + b + c \(⋮3\)

\(a)\)

\(\left(x-1\right)\left(x^3+x^2+x+1\right)\)

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

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

\(=x^4-1\)

\(b)\)

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

\(=x^5+1^5\)

\(=x^5+1\)

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

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

\(=\left[\left(2x-y\right)^2.\left(2x-y\right)-3x.\left(y-2x\right)^2\right]-\left(2x-y\right)^2\)

\(=\left[\left(y-2x\right)^2.\left(2x-y-3x\right)\right]-\left(2x-y\right)^2\)

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

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

Chúc bạn học tốt 

phân tích đa thức

(2x – y)^3 – 3x(y – 2x)2 – 4x2 + 4xy – y ^2  

= -(y-2x)^2(y+x+1)

đây nha bạn 

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

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

\(=\left(2x-y\right)^3-\left(2x-y\right)^2\left(3x+1\right)\)

\(=\left(2x-y\right)^2\left(2x-y-3x-1\right)\)

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

\(\left(x-3\right)\left(4x-1\right)\left(6x-2\right)\left(2x+1\right)\)

\(\left(4x^2-12x-x+3\right)\left(12x^2-4x+6x-2\right)\)

\(\left(4x^2-13x+3\right)\left(12x^2+2x-2\right)\)

\(48x^4-13x^3+36x^2-156x^3-26x^2+26x-8x^2+26x-6\)

\(48x^4-169x^3+2x^2+52x-6\)

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

\(\left(x-3\right)\left(4x-1\right)-\left(6x+2\right)\left(2x-1\right)\)

\(=4x^2-x-12x+3-\left(12x^2-6x+4x-2\right)\)

\(=4x^2-x-12x+3-12x^2+6x-4x+2\)

\(=-8x^2-11x+5\)