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因式分解(x²-y²)²-8(x²+y²)+16
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(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)
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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 )
= ( 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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