一道数学题,最好巧算.计算:(x-y+2)2-(x-y-2)2((x-y+2)2是指x-y+2的平方,(x-y-2)2是指x-y-2的平方)

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/23 23:11:45
一道数学题,最好巧算.计算:(x-y+2)2-(x-y-2)2((x-y+2)2是指x-y+2的平方,(x-y-2)2是指x-y-2的平方)一道数学题,最好巧算.计算:(x-y+2)2-(x-y-2)

一道数学题,最好巧算.计算:(x-y+2)2-(x-y-2)2((x-y+2)2是指x-y+2的平方,(x-y-2)2是指x-y-2的平方)
一道数学题,最好巧算.
计算:(x-y+2)2-(x-y-2)2
((x-y+2)2是指x-y+2的平方,(x-y-2)2是指x-y-2的平方)

一道数学题,最好巧算.计算:(x-y+2)2-(x-y-2)2((x-y+2)2是指x-y+2的平方,(x-y-2)2是指x-y-2的平方)
(x-y+2)2-(x-y-2)2
平方差公式
=【(x-y+2)-(x-y-2)】【(x-y+2)+(x-y-2)】
=4×(2x-2y)
=8x-8y

用平方差公式
a²-b²
=(a+b)x(a-b)

(x-y+2)2-(x-y-2)2
=(x-y+2+x-y-2)x(x-y+2-x+y+2)
=(2x-2y)x4
=8x-8y