Question

因式分解:(1-x²)(1-y²)-4xy

Answer 1

(1-x²)(1-y²)-4xy
解：
原式=1-x²-y²+x²y²-4xy
=-（x²+2xy+y²)+x²y²-2xy+1
=-(x+y)²+(xy-1)²
=(xy-1)²-(x+y)²
=(xy-1-x-y)(xy-1+x+y)
=(xy-x-y-1)(xy+x+y-1)

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Answer 2

(1-x^2)(1-y^2)-4xy
=1-x^2-y^2+x^2y^2-4xy
=-(x^2+2xy+y^2)+(x^2y^2-2xy+1)
=(xy-1)^2-(x+y)^2
=(xy+x+y-1)(xy-x-y-1)

Answer 3

(1-x²)(1-y²)-4xy
=1-x²-y²+x²y²-4xy
=（1-2xy+x²y²）-（x²+2xy+y²）
=（xy-1）^2-(x+y)^2
=(xy-1+x+y)(xy-1-x-y)

Answer 4

(1-x²)(1-y²)-4xy
=1-x²-y²+x²y²-4xy
=(1-2xy+x²y²)-(x²+y²+2xy)
=(1-xy)²-(x+y)²
=(1-xy+x+y)(1-xy-x-y)

Answer 5

(1-X^2)(1-Y^2)-4XY
=1 - X^2 - Y^2 + X^2 * Y^2 - 4XY
=( 1 - 2XY + X^2 * Y^2 ) - ( X^2 + 2XY + Y^2 )
=( 1 - XY )^2 - ( X + Y )^2
=( 1 - XY + X + Y )( 1 - XY - X - Y )