Đáp án:
a) x² - y² - 2x + 2y
= ( x - y ) ( x + y ) - 2 ( x - y )
= ( x - y ) ( x + y ) - 2
b) 2x + 2y - x² - xy
= ( 2x - x² ) + ( 2y - xy )
= x ( 2 - x ) + y ( 2 - x )
= ( x + y ) ( 2 - x )
c ) 3a² - 6ab + 3b² - 12c²
= 3 ( a² - 2ab + b² - 4c² )
= 3 [ ( a - b )² - (2c)² ]
= 3 ( a - b - 2c ) ( a - b + 2c )
d) x² - 25 + y² + 2xy
= ( x² + 2xy + y² ) - 5²
= ( x + y )² - 5²
= ( x + y - 5 ) ( x + y + 5 )
e) a² + 2ab + b² - ac - bc
= ( a + b )² - c ( a + b )
= ( a + b ) ( a + b - c )
f) x² - 2x - 4y² - 4y
= x² - 2x + 1 - 4y² - 4y - 1
= ( x² - 2x + 1 ) - [ ( 2y)² + 4y + 1 ]²
= ( x - 1 )² - ( 2y + 1 )²
= ( x - 1 - 2y - 1 ) ( x- 1 + 2y + 1 )
g) x²y - x³ - 9y + 9x
= x² ( y - x ) - 9( y - x )
= ( y - x ) ( x² - 9 )
= ( y - x ) ( x² - 3 ) = ( y - x ) ( x - 3 ) ( x + 3 )
h) x² ( x - 1 ) + 16 ( 1 - x )
= x² ( x - 1 ) - 16 ( x - 1 )
= ( x - 1 ) (x² - 16 )
= ( x - 1 ) ( x² -4² )
= ( x - 1 ) ( x - 4 ) ( x + 4 )
Giải thích các bước giải:
