Maths.

Should no. 1 be x(2xy2 –y2)-y(x –2x2)?
(1) x(2xy2 –y2)-y(x –2x2)
=xy2( 2x – 1 ) – xy ( 1 – 2x )
=xy2( 2x – 1 ) + xy ( 2x – 1 )
=( xy2 + xy )( 2x – 1 ) [ Take ( 2x – 1 ) as common factor. ]
= xy ( y + 1 )( 2x – 1 )
(2) (px+q)2-(2px+ 2q)
= ( px + q )2 – 2 ( px + q )
= ( px + q )[ ( px + q ) – 2 ] [ Take ( px + q ) as common factor. ]
= ( px + q )( px + q – 2 )
(3) (2x-y)(a2+b)-(b-a2)(y-2x)
= ( 2x – y )( a2 + b ) + ( b – a2 )( 2x – y )
= ( 2x – y )( a2 + b + b – a2 ) [ Take ( 2x – y ) as common factor. ]
= 2b ( 2x – y )
(4) [(x+y)2 / 2] -x(x+ y)
= ( 1 / 2 ) [ ( x + y )2 – 2x ( x + y ) ]
= ( 1 / 2 )( x + y )[ ( x + y ) – 2x ] [ Take ( x + y ) as common factor. ]
= ( 1 / 2 )( x + y )( - x + y )
= ( y – x )( x + y ) / 2

2007-09-17 23:25:54 補充：
Sorry for misunderstanding Q1: x(2xy^2-y^2)-y(x^2-2x^2)= x( 2xy^2 - y^2 ) - y ( - x^2 ) = x ( 2xy^2 - y^2 ) + x^2y = 2x^2y^2 - xy^2 + x^2y [ Expand and simplify ] = xy ( 2xy - y + x ) [ Take xy as the common factor. ]

1.x(2xy^2-y^2)-y(x^2-2x^2)
=2x^2 y^2-xy^2+x^2 y
=xy(2xy^2-y^2+x)
2.(px+q)^2-(2px+2q)
=(px+q)[px+q-2]
3(2x-y)(a^2 b)-(b-a^2)(y-2x)
=(2x-y)(a^2+b)+(2x-y)(b-a^2)
=(2x-y)(a^2+b+b-a^2)
=(2x-y)(2b)
4.(x+y)^2/2-x(x+y)
=(x+y)(x/2+y/2-x)
=(x+y)(-x/2+y/2)