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分解因式：x^2-6xy+9y^2-3x+9y+2
题目详情
分解因式：x^2-6xy+9y^2-3x+9y+2
▼优质解答
答案和解析
x" - 6xy + 9y" - 3x + 9y + 2
= ( x" - 3xy - 3xy + 9y" ) - (3x - 9y) + 2
= x( x - 3y ) - 3y( x - 3y ) - 3( x - 3y ) + 2
= ( x - 3y )" - ( x - 3y ) - 2( x - 3y ) + 2
= ( x - 3y )( x - 3y - 1 ) - 2( x - 3y - 1 )
= ( x - 3y - 1 )( x - 3y - 2 )
= ( x" - 3xy - 3xy + 9y" ) - (3x - 9y) + 2
= x( x - 3y ) - 3y( x - 3y ) - 3( x - 3y ) + 2
= ( x - 3y )" - ( x - 3y ) - 2( x - 3y ) + 2
= ( x - 3y )( x - 3y - 1 ) - 2( x - 3y - 1 )
= ( x - 3y - 1 )( x - 3y - 2 )
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