【因式分解】三道题①9x的四次方-82x²+9②x的三次方-x²-y的三次方+y² ③x²-6xy+9y²-3x+9y

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【因式分解】三道题①9x的四次方-82x²+9②x的三次方-x²-y的三次方+y²③x²-6xy+9y²-3x+9y【因式分解】三道题①9x的四次方-

【因式分解】三道题①9x的四次方-82x²+9②x的三次方-x²-y的三次方+y² ③x²-6xy+9y²-3x+9y
【因式分解】三道题
①9x的四次方-82x²+9
②x的三次方-x²-y的三次方+y²
③x²-6xy+9y²-3x+9y

【因式分解】三道题①9x的四次方-82x²+9②x的三次方-x²-y的三次方+y² ③x²-6xy+9y²-3x+9y
=(9x^2-1)(x^2-9)=(3x+1)(3x-1)(x+1)(x-1)
=(x^3-y^3)-(x^2-y^2)=(x-y)(x^2+xy+y^2)-(x-y)(x+y)=(x-y)(x^2+xy+y^2-x-y)
=(x-3y)^2-3(x-3y)=(x-3y)(x-3y-3)

3) (x-3y)2-3(x-3y)
=(x-3y)(x-3y-3)

①9x的四次方-82x²+9
=(9x^2-1)(x-9)
②x的三次方-x²-y的三次方+y²
=x^3-y^3-(x^2-y^2)
=(x-y)(x^2+xy+y^2)-(x-y)(x+y)
=(x-y)(x^2+xy+y^2-x-y)
③x²-6xy+9y²-3x+9y
=(x-3y)^2-3(x-3y)
=(x-3y)(x-3y-3)

(3x+1)(3x-1)(x-3)(x+3)
(x-y)(x+xy+y-x-y)
(x-3y)(x-3y-3)