Rút gọn a) (x+y)^2+(x-y)^2 b)2(x-y)(x+y)+(x+y)^2+(x-y)^2 c)(x-y+z)^2+(z-y)^2+2(x-y+z)(y-z) d)(5x-1)+2(1-5x)(4+5x)+(5x+4)^2 e)(x-y)^3+(y+x)^3+(y-x)^3-

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1. a)(x+y)² + (x-y)²

   <=>{(x+y) + (x-y)}{(x+y) – (x-y) }

   <=>(x + y + x – y) ( x +y – x +y )

   <=>           2x       .   2y

   <=>                   4xy

   b)2(x-y)(x+y) + (x+y)² + (x-y)²

   <=>2(x²-y²) + x² + 2xy + y² + x² + y² – 2xy

   <=>2(x²-y²) + 2(x²+y²)

   <=>2 (x²-y²+x²+y²)

   <=>4x²

   c)(x-y+z)² + (z-y)² + 2(x-y+z)(y-z)

   <=>(x-y+z)² – 2(x-y+z)(y-z) + (z-y)² 

   <=> (x-y+z-z+y)²
   <=>x²

   d)(5x-1)+2(1-5x)(4-5x)+(5x+4)²

   <=>5x-1+(2-10x)(4-5x)+25x² +25x*4+16

   <=>5x-1+8+10x-40x-50x² +25x² + 100x +16

   <=>-25x²+75x+23

   e)(x-y)³+(y+x)³+(y-x)³-3xy(x+y)

   <=>(x³-3x²y + 3xy²-y³)+(y³+3x²y+3xy²+x³)+(y³-3y²x+3yx²-x³)-3x²y-3xy²

   <=>x³ + y³

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