Bài 1
( x - y )2 - 4
= ( x - y )2 - 22
= ( x - y - 2 )( x - y + 2 )
x2 - 16( x + y )2
= x2 - 42( x + y )2
= x2 - ( 4x + 4y )2
= ( x2 - 4x - 4y )( x2 - 4x + 4y )
8x3 + 36x2y + 54xy2 + 27y3
= ( 2x )3 + 3.( 2x )2.3y + 3.2x.( 3y )2 + ( 3y )3
= ( 2x + 3y )3
Bài 2.
a) ( x2 + 4 )( x2 - 4 ) - ( x2 + 1 )( x2 - 1 )
= [ ( x2 )2 - 42 ] - [ ( x2 )2 - 12 ]
= x4 - 16 - x4 + 1
= -15
b) ( y - 3 )( y + 3 )( y2 + 9 )( y2 + 2 )( y2 - 2 )
= [ ( y - 3 )( y + 3 )( y2 + 9 ) ][ ( y2 + 2 )( y2 - 2 ) ]
= { [ ( y - 3 )( y + 3 ) ]( y2 + 9 ) }[ ( y2 )2 - 22 ]
= [ ( y2 - 9 )( y2 + 9 ) ]( y4 - 4 )
= ( y4 - 81 )( y4 - 4 )
= y4( y4 - 4 ) - 81( y4 - 4 )
= y8 - 4y4 - 81y4 + 324
= y8 - 85y4 + 324
