a) 5x2 - 5xy + 7y - 7x = ( 5x2 - 5xy ) - ( 7x - 7y ) = 5x( x - y ) - 7( x - y ) = ( x - y )( 5x - 7 )
b) x2 - y2 + 2x + 1 = ( x2 + 2x + 1 ) - y2 = ( x + 1 )2 - y2 = ( x - y + 1 )( x + y + 1 )
c) 3x2 + 6xy + 3y2 - 3z2 = 3( x2 + 2xy + y2 - z2 ) = 3[ ( x2 + 2xy + y2 ) - z2 ] = 3[ ( x + y )2 - z2 ] = 3( x + y - z )( x + y + z )
d) ab( x2 + y2 ) + xy( a2 + b2 ) = abx2 + aby2 + a2xy + b2xy
= ( a2xy + abx2 ) + ( aby2 + b2xy )
= ax( ay + bx ) + by( ay + bx )
= ( ay + bx )( ax + by )