Question

分式因解：(x+2y)^2+6(x+2y)(y-x)+9(x-y)^2

Answer 1

解：分式因解：(x+2y)^2+6(x+2y)(y-x)+9(x-y)^2
=(x+2y)(x+2y+6y-6x)+9(x-y)^2
=(x+2y)(8y-5x)+9(x-y)^2
=8xy-5x^2+16y^2-10xy+9x^2+18xy-9y^2
=16xy+4x^2+7y^2
=[(2x)^2+2*2x*4y+(4y)^2]-9y^2
=(2x+4y)^2-(3y)^2
=(2x+4y+3y)(2x+4y-3y)
=(2x+7y)(2x+y)

Answer 2

(x+2y)^2+6(x+2y)(y-x)+9(x-y)^2
=(x+2y)²+6(x+2y)(y-x)+[3(y-x)²]
=[x+2y+3(y-x)][(x+2y-3(y-x))]
=(5y-2x)(4x-y)

追问

那我再问一道：a^2-4ab+4b^2-2a+4b

谢谢谢谢！

追答

不客气，
a^2-4ab+4b^2-2a+4b

=(a²-4ab+4b²)-2(a-2b)
=(a-2b)²-2(a-2b)
=(a-2b-2)(a-2b)

请采纳。