Question

Phân tích đa thức thành nhân tử

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

b) \(3a^2x-3a^2y+abx-aby\)

Answer 1

a) x(y - x)³ + y(x - y)² + xy(x - y)

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

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

= (x - y)[x(y - x)(x - y) + y(x - y) + xy]

= (x - y)[x(y - x)(x - y) + y(x - y) + xy]

b) 3a²x - 3a²y + abx - aby

= 3a²(x - y) + ab(x - y)

= a(x - y)(3a + b)

Answer 2

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

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

= ( x - y )[ -x( x - y )² - y( x - y ) + xy ]

= ( x - y )[ -x( x² - 2xy + y² ) - yx + y² + xy ]

= ( x - y )( -x³ + 2x²y - xy² - yx + y² + xy )

= ( x - y )( -x³ + 2x²y - xy² + y² )

b) 3a²x - 3a²y + abx - aby

= 3a²( x - y ) + ab( x - y )

= ( x - y )( 3a² + ab )

= ( x - y )a( 3a + b )

Answer 3

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

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

= (x - y) [-x (x - y) 2  - y (x - y) + xy]

= (x - y) [-x (x 2  - 2xy + y 2  ) - yx + y 2  + xy]

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

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

b) 3a 2 x - 3a 2 y + abx - aby

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

= (x - y) (3a 2  + ab)

= (x - y) a (3a + b)học tốt