因式分解(x²-y²）²-8（x²+y²）+16

因式分解(x²-y²）²-8（x²+y²）+16
因式分解(x²-y²）²-8（x²+y²）+16

因式分解(x²-y²）²-8（x²+y²）+16
(x²-y²）²-8（x²+y²）+16=(x²+y²）²-8（x²+y²）+16-4x²y²=（x²+y²-4）²-4x²y²=（x²+y²-4+2xy）（x²+y²-4-2xy）=[(x+y)²-4][(x-y)²-4]=(x+y+2)(x+y-2)(x-y+2)(x-y-2)

( x" - y" )" - 8( x" + y" ) + 16
= ( x" + y" )" - 4x"y" - 8( x" + y" ) + 16
= ( x" + y" )" - 2X4X( x" + y" ) + 4" - 4x"y"
= [ ( x" + y" ) - 4 ]" - ( 2xy )"
= [ ( x" + y" - 4 ) + 2xy ][...

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( x" - y" )" - 8( x" + y" ) + 16
= ( x" + y" )" - 4x"y" - 8( x" + y" ) + 16
= ( x" + y" )" - 2X4X( x" + y" ) + 4" - 4x"y"
= [ ( x" + y" ) - 4 ]" - ( 2xy )"
= [ ( x" + y" - 4 ) + 2xy ][ ( x" + y" - 4 ) - 2xy ]
= ( x" + y" - 4 + 2xy )( x" + y" - 4 - 2xy )
= [ ( x + y )" - 2" ][ ( x - y )" - 2" ]
= ( x + y + 2 )( x + y - 2 )( x - y + 2 )( x - y - 2 )

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