16) 2x + 2y - x2 - xy = ( 2x + 2y ) - ( x2 + xy ) = 2( x + y ) - x( x + y ) = ( x + y )( 2 - x )
17) x2 - 2x - 4y2 - 4y = ( x2 - 4y2 ) - ( 2x + 4y ) = ( x - 2y )( x + 2y ) - 2( x + 2y ) = ( x + 2y )( x - 2y - 2 )
18) x2y - x3 - 9y + 9x = ( x2y - x3 ) - ( 9y - 9x ) = x2( y - x ) - 9( y - x ) = ( y - x )( x2 - 9 ) = ( y - x )( x - 3 )( x + 3 )
19) x2( x - 1 ) + 16( 1 - x ) = x2( x - 1 ) - 16( x - 1 ) = ( x - 1 )( x2 - 16 ) = ( x - 1 )( x - 4 )( x + 4 )
20) 2x2 + 3x - 2xy - 3y = ( 2x2 - 2xy ) + ( 3x - 3y ) = 2x( x - y ) + 3( x - y ) = ( x - y )( 2x + 3 )
20, \(2x^2+3x-2xy-3y=2x\left(x-y\right)+3\left(x-y\right)=\left(2x+3\right)\left(x-y\right)\)
16, \(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
17, \(x^2-2x-4y^2-4y=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)=\left(x-2y-2\right)\left(x+2y\right)\)
18, \(x^2y-x^3-9y+9x=-x\left(x^2-9\right)+y\left(x^2-9\right)=\left(-x-y\right)\left(x^2-9\right)=\left(y-x\right)\left(x-3\right)\left(x+3\right)\)
19, \(x^2\left(x-1\right)+16\left(1-x\right)=x^2\left(x-1\right)-16\left(x-1\right)=\left(x^2-16\right)\left(x-1\right)=\left(x-4\right)\left(x+4\right)\left(x-1\right)\)
Bài 1: Phân tích đa thức thành nhân tử bằng phương pháp đặt nhân tử chung
16) 2x + 2y - x2 - xy
= ( 2x - x2 ) + ( 2y - xy )
= x ( 2 - x ) + y ( 2 - x )
= ( 2 - x ) ( x + y )
17) x2 - 2x - 4y2 - 4y
= ( x2 - 4y2 ) - ( 2x + 4y )
= ( x - 2y ) ( x + 2y ) - 2 ( x + 2y )
= ( x + 2y ) ( x - 2y - 2 )
18) x2y - x3 - 9y +9x
= ( 9x + x3 ) + ( x2y - 9y )
= x ( 9 + x2 ) + y ( x2 - 9 )
= x ( 9 + x2 ) - y ( 9 + x2 )
= ( 9 + x2 ) ( x - y )
= ( 3 - x ) ( 3 + x ) ( x - y )
19) x2 ( x - 1) + 16 (1 - x )
= x2 ( x - 1 ) - 16 ( x - 1 )
= ( x - 1 ) ( x2 - 16 )
= ( x - 1 ) ( x - 4 ) ( x + 4 )
20) 2x2 + 3x - 2xy - 3y
= 2x2 + 3x - ( 2xy + 3y )
= x ( 2x + 3 ) - y ( 2x + 3 )
= ( 2x + 3 ) ( x - y )
