1; 49 . ( y - 4 )2 - 9. ( y - 2 )2
= [ 7 . ( y - 4 ) ]2 - [ 3 .( y - 2 ) ]2
= ( 7y - 28 )2 - ( 3y - 6 )
= [( 7y - 28 ) - ( 3y - 6 )] . [( 7y -28 ) + ( 3y - 6 )
= ( 7y - 28 - 3y + 6 ) . ( 7y -28 + 3y - 6 )
= ( 4y - 22 ) . ( 10y - 34 )
2; ( a + 1 )3 - 1 = ( a + 1 )3 - 13
= ( a + 1 - 1 ) . [( a + 1 )2 + ( a + 1 ) . 1 + 12 ]
= a . ( a2 + 2a + 1 + a + 1 + 1 )
= a . ( a2 + 3a + 3 )
3; x3 + 3x2 + 3x + 1 - 27z3
= ( x + 1 ) 3 - ( 3z )3
= ( x + 1 - 3z ) . [( x + 1 )2 + ( x + 1 ) . 3z + (3z)2 ]
= ( x + 1 - 3z ) . ( x2 + 2x + 1 + 3xz + 3z + 9z2 )
4; 8x2 + 30x + 7 = 8x2 + 2x + 28x + 7
= ( 8x2 + 2x ) + ( 28x + 7 )
= 2x . ( 4x + 1 ) + 7 . ( 4x + 1 )
= ( 4x + 1 ) . ( 2x + 7 )
5; x2 + 3x - 18 = x2 + 6x - 3x - 18
= ( x2 + 6x ) - ( 3x + 18 )
= x . ( x + 6 ) - 3 . ( x + 6 )
= ( x + 6 ) . ( x - 3 )
6; x2 - 2x - 3 = x2 - x + 3x - 3
= ( x2 - x ) + ( 3x - 3 )
= x . ( x - 1 ) + 3 . ( x - 1 )
= ( x - 1 ) . ( x + 3 )