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中學maths

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1. (x^4+12x-4x^2-9) 2. [4y^2z^2-(y^2+z^2-x^2)] 3. (x^2-xy)^2-(xy-y^2)^2

最佳解答:

Q1) x^4 + 12x - 4x^2 - 9 = x^4 - (4x^2 - 12x + 9) = x^4 - [ (2x)^2 - 2(2x)(3) +(3)^2 ] = x^4 - ( 2x - 3 )^2 = [ x^2 - 2x + 3 ][ x^2 + 2x - 3 ] = [ x^2 - 2x + 3 ]( x+3 )( x-1 ) Q2) 4y^2 z^2 - ( y^2 + z^2 - x^2 ) = 4y^2 z^2 - ( y^2 + z^2 - x^2 +2yz - 2yz ) = 4y^2 z^2 - ( (y+z)^2 - 2yz - x^2 ) = 4y^2 z^2 - (y+z)^2 + 2yz + x^2 = 4y^2z^2 + 2yz + x^2 - (y+z)^2 = 2yz( 2yz + 1 ) + ( x+y+z )( x-y-z ) OR 4y^2 z^2 - ( y^2 + z^2 - x^2 ) = 4y^2 z^2 - ( y^2 + z^2 - x^2 +2yz - 2yz ) = 4y^2 z^2 - ( (y-z)^2 + 2yz - x^2 ) = 4y^2 z^2 - (y-z)^2 - 2yz + x^2 = 4y^2z^2 - 2yz + x^2 - (y-z)^2 = 2yz( 2yz - 1 ) + ( x+y-z )( x-y+z ) Q3) ( x^2 - xy )^2 - ( xy - y^2 )^2 = ( x^2 - xy + xy - y^2 )( x^2 - xy - xy + y^2 ) = ( x^2 - y^2 )( x^2 - 2xy + y^2 ) = ( x-y )( x+y ) ( x-y )^2 = ( x+y )( x-y )^3

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