Question

9(x+2y)^2-25(x-2y)^2=【 】^2-【 】^2=________.

Answer 1

9(x+2y)²-25(x-2y)²
=【3(x+2y)】²-【5(x-2y)】²
=[3(x+2y)+5(x-2y)][3(x+2y)-5(x-2y)]
=(8x-4y)(-2x+16y)
=-8(2x-y)(x-8y)

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追问

[3(x+2y)+5(x-2y)][3(x+2y)-5(x-2y)]

为什么得：
(8x-4y)(-2x+16y)

追答

[3(x+2y)+5(x-2y)][3(x+2y)-5(x-2y)]
=(3x+6y+5x-10y)(3x+6y-5x+10y)
=(8x-4y)(-2x+16y)

Answer 2

9(x+2y)^2-25(x-2y)^2

=[3(x+2y)]^2-[5(x-2y)]^2
=[3(x+2y)+5(x-2y)][3(x+2y)-5(x-2y)]
=(8x-4y)(-2x+16y)
=-8(2x-y)(x-8y)

Answer 3

9(x+2y)^2-25(x-2y)^2=【3(x+2y) 】^2-【5(x-2y) 】^2=__-8（2x-y)(x-8y)_____.