Question

phân tích các đa thức sau thành nhân tử

a) \(9\left(a+b\right)^2-\left(a+b\right)\)

b) \(\left(mx+my\right)+\left(3x+3y\right)\)

c) \(\left(12xy\right)-6x-\left(2y-1\right)\)

d) \(\left(7xy^2-5x^2y\right)+\left(5x-7y\right)\)

e) \(2x\left(x-y\right)-\left(4x-4y\right)\)

Answer 1

9(a + b)² - (a + b) = (a + b)[9(a + b) - 1]

(mx + my) + (3x + 3y) = m(x + y) + 3(x + y) = (m + 3)(x + y)

(12xy) - 6x - (2y - 1) = 6x(2y - 1) - (2y - 1) = (6x - 1)(2y - 1)

(7xy² - 5x²y) + (5x - 7y) = xy(7y - 5x) + (5x - 7y) = -xy(5x - 7y) + (5x - 7y) = (-xy + 1)(5x - 7y)

2x(x - y) - (4x - 4y) = 2x(x - y) - 4(x - y) = (2x - 4)(x - y)

Answer 2

a) 9( a + b )² - ( a + b ) = ( a + b )[ 9( a + b ) - 1 ]

b) ( mx + my ) + ( 3x + 3y ) = m( x + y ) + 3( x + y ) = ( m + 3 )( x + y )

c) 12xy - 6x - ( 2y - 1 ) = 6x( 2y - 1 ) - ( 2y - 1 ) = ( 6x - 1 )( 2y - 1 )

d) ( 7xy² - 5x²y ) + ( 5x - 7y ) = xy( 7y - 5x ) + ( 5x - 7y ) = -xy( 5x - 7y ) + ( 5x - 7y ) = ( -xy + 1 )( 5x - 7y )

e) 2x( x - y ) - ( 4x - 4y ) = 2x( x - y ) - 4( x - y ) = ( 2x - 4 )( x - y )