Question

(x-2y+3)(x+2y-3)-(-x+2y)的平方=?

(x-2y+3)(x+2y-3)-(-x+2y)^2=?

Answer 1

(x-2y+3)(x+2y-3)-(-x+2y)^2
=[x-(2y-3)][x+(2y-3)]-(x-2y)^2
=x^2-(2y-3)^2-(x-2y)^2 (平方差公式)
=x^2-(4y^2-12y+9)-(x^2-4xy+4y^2) (完全平方公式)
=-8y^2+4xy+12y-9 (合并同类项)

Answer 2

(x-2y+3)(x+2y-3)-(-x+2y)^2
=(x-2y+3)(x+2y-3)-(x-2y)^2
=[x-(2y-3)][x+(2y-3)]-(x-2y)^2
=x^2-(2y-3)^2-(x-2y)^2
=x^2-(x-2y)^2-(2y-3)^2
=(x+x-2y)(x-x+2y)-(2y-3)^2
=4y(x-y)-4y^2+12y-9
=4xy-4y^2-4y^2+12y-9
=4xy-8y^2+12y-9

追问

有朋友提供﹙x－2y＋3﹚﹙x＋2y－3﹚－﹙﹣x＋2y﹚²
＝[x－﹙2y－3﹚][x＋﹙2y－3﹚]－﹙x－2y﹚²
＝x²－﹙2y－3﹚²－﹙x－2y﹚²
＝x²－4y²＋12y－9－x²＋4y－4y²
＝﹣8y²＋16y－9
你认为呢?

追答

﹙x－2y﹚²你说等于什么

Answer 3

解：﹙x－2y＋3﹚﹙x＋2y－3﹚－﹙﹣x＋2y﹚²
＝[x－﹙2y－3﹚][x＋﹙2y－3﹚]－﹙x－2y﹚²
＝x²－﹙2y－3﹚²－﹙x－2y﹚²
＝x²－4y²＋12y－9－x²＋4y－4y²
＝﹣8y²＋16y－9

Answer 4

自己算不要怕累