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因式分解x^2-9y^2-4x+4 x^4-25x^2+60x-36
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因式分解x^2-9y^2-4x+4 x^4-25x^2+60x-36
▼优质解答
答案和解析
x" - 9y" - 4x + 4
= x" - 4x + 4 - 9y"
= x" - 2x - 2x + 4 - 9y"
= x( x - 2 ) - 2( x - 2 ) - 9y"
= ( x - 2 )" - ( 3y )"
= ( x + 3y - 2 )( x - 3y - 2 )
x^4 - 25x" + 60x - 36
= x^4 - [ 25x" - 60x + 36 ]
= x^4 - [ 25x" - 30x - 30x + 36 ]
= x^4 - [ 5x( 5x - 6 ) - 6( 5x - 6 ) ]
= ( x" )" - ( 5x - 6 )"
= ( x" + 5x - 6 )( x" - 5x + 6 )
= ( x" - x + 6x - 6 )( x" - 2x - 3x + 6 )
= [ x( x - 1 ) + 6( x - 1 ) ][ x( x - 2 ) - 3( x - 2 ) ]
= ( x + 6 )( x - 1 )( x - 2 )( x - 3 )
= x" - 4x + 4 - 9y"
= x" - 2x - 2x + 4 - 9y"
= x( x - 2 ) - 2( x - 2 ) - 9y"
= ( x - 2 )" - ( 3y )"
= ( x + 3y - 2 )( x - 3y - 2 )
x^4 - 25x" + 60x - 36
= x^4 - [ 25x" - 60x + 36 ]
= x^4 - [ 25x" - 30x - 30x + 36 ]
= x^4 - [ 5x( 5x - 6 ) - 6( 5x - 6 ) ]
= ( x" )" - ( 5x - 6 )"
= ( x" + 5x - 6 )( x" - 5x + 6 )
= ( x" - x + 6x - 6 )( x" - 2x - 3x + 6 )
= [ x( x - 1 ) + 6( x - 1 ) ][ x( x - 2 ) - 3( x - 2 ) ]
= ( x + 6 )( x - 1 )( x - 2 )( x - 3 )
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