Question

PTĐTTNT

a/ 2xy + 5x^2y - x^3y

b/ ( x + y )^2 - 9x^2

c/ 2 . ( x - y ) + xy - x^2 

d/ 3x + 3y - x^2 - 2xy - y^2

e/ x^3 + 3x^2y + 3xy^2 + y^3 - x -y

f/ x^3 + y^3 - 2 . ( x^2 - y^2 )

g/ x^2 . ( x - 2 ) + 4 . ( 2 - x )

Answer 1

a) 2xy + 5x^2y - x^3y=y(2x+5x²-x³)

b/ ( x + y )^2 - 9x^2=(x²+2xy+y²)-9x²=-8x²+2xy+y²

c/ 2 . ( x - y ) + xy - x^2 =2x-2y+xy-2x=-x²+2x+xy-2y

d/ 3x + 3y - x^2 - 2xy - y^2=−(x²+2xy+y²)+3(x+y)=−(x+y)²+3(x+y)

e/ x^3 + 3x^2y + 3xy^2 + y^3 - x -y=(x+y)³−(x+y)=(x+y)((x+y)²−1)=(x+y)(x+y−1)(x+y+1)

f/ x^3 + y^3 - 2 . ( x^2 - y^2 )=x³+y³−2(x²−y²)=(x+y)(x²−xy+y²)−2(x−y)(x+y)=(x+y)[(x²−xy+y²)−2(x−y)]

g/ x^2 . ( x - 2 ) + 4 . ( 2 - x )=x³−2x²+8−4x=x³−2x²−4x+8

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