Bài 1: Phân tích các đa thức sau thành nhân tử
a) 36x2 - (3x - 2)2
b) 16(4x + 5)2 - 25(2x + 2)2
c) (x - y + 4)2 - (2x + 3y - 1)2
d) (x + 1)4 - (x - 1)4
e) 16x2 - 24xy + 9y2
f) -x4/4 + 2x2y3 - 4y6
g) 64x3 + 1
h) x3y6z9 - 125
k) 27x6 - 8x3
l) x6 - y6
m) 27x3 - 54x2y + 36xy2 - 8y3
n) y9 - 9x2y6 + 27x4y3 - 27x6
a ) 36x2 - ( 3x - 2 )2
= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )
= ( 3x + 2 ) ( 9x - 2 )
b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2
= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]
= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )
= ( 26x + 15 ) ( 6x - 5 )
a ) 36x2 - ( 3x - 2 )2
= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )
= ( 3x + 2 ) ( 9x - 2 )
b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2
= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]
= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )
= ( 26x + 15 ) ( 6x - 5 )