a) \(x^2-x-y^2+y\)

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

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

b) \(x^2-2xy-z^2+y^2\)

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

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

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

c) \(5x-5y+ax-ay\)

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

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

a) x² - x - y² - y

= (x^2 - y^2) - (x+y)

= (x+y) (x-y) - (x+y)

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

b) x² - 2xy - z² + y²

= (x^2 - 2xy + y^2 ) - z^2 

= (x-y)^ 2- z^2

= (x-y-z) (x-y+z)

c) 5x - 5y + ax - ay

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

= (5+a)(x-y)

a) x² - x - y² - y  =  (x² - y²) - (x+y) = (x-y)(x+y) - (x+y) = (x+y). ( x- y - 1)

b) x² - 2xy - z² + y²  = (x² - 2xy + y² ) - z² = (x-y)² - z² = (x-y+z) . (x-y-z)

c) 5x - 5y + ax - ay = 5.(x-y) + a(x-y) = (5+a) . ( x-y) 

a) \(2xy-y+6x-3=\left(2xy+6x\right)-\left(y+3\right)=2x\left(y+3\right)-\left(y+3\right)=\left(2x-1\right)\left(y+3\right)\)

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

x(y - z) + 2(z - y)

= x(y - z) - 2(y - z)

= (x - 2)(y - z)

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

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

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

= 2x(2x - 3y)

1/\(x\left(y-z\right)+2\left(z-y\right)\)\(=\left(y-z\right)\left(x-2\right)\)

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

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

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

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

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

a) \(x^2+4x-y^2+4\)

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

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

c) \(x^2-2xy+y^2-z^2+2zt-t^2\)

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

\(=\left(x-y-z+t\right)\left(x-y+z-t\right)\)

a) x² + 4x - y² + 4 = (x² + 4x + 4) - y² = (x + 2)² - y = (x + 2 - y)(x + 2 + y)

b) 3x² + 6xy + 3y² - 3z² = 3(x² + 2xy + y² - z²) = 3[(x² + 2xy + y²) - z²) = 3[(x + y)² - z) = 3(x + y + z)(x + y - z)²

c:   x^6 - y^6 

= (x^3)^2 - (y^3)^2 

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

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

 a:   x^2 + 4y^2 + 4xy

= x^2 + 4xy + 4y^2

= (x+2y)^2

Mình cảm ơn nha. Bạn giải đc ý b k ạ

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

\(\text{ Phân tích thành nhân tử}\)

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

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

\(\text{ Phân tích thành nhân tử}\)

\(\left(-\left(y-x+1\right)\right)\left(y+x\right)\)

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

\(\text{ Phân tích thành nhân tử}\)

\(\left(-\left(y-x+1\right)\right)\left(y+x\right)\)

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

\(\text{ Phân tích thành nhân tử}\)

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

1) \(x^2-4y^2+4x+8y=\left(x-2y\right)\left(x+2y\right)+4\left(x+2y\right)=\left(x+2y\right)\left(x-2y+4\right)\)