\x0d如图,ABCD是边长为a的正方形.\x0dAEFG是边长为2b的正方形.\x0dAGJH是边长为2b的正方形.\x0d\x0d我们先证明S1和S3两个矩形面积相等.\x0d显然,JG = FE = 2b\x0dDG = AD-AG = (a-2b)\x0dEB = AB-AE = (a-2b)\x0d即：DG = EB\x0d可见,S1、S3长宽都相等,所以面积相等.\x0d\x0dS1+S2 = IC*IJ = (a+2b)(a-2b)\x0d\x0dS3+S2 = (S2+S3+S4)-S4\x0d= ABCD的面积 - AEFG的面积\x0d= a^2 - (2b)^2 = a^2 - 4b^2\x0d\x0d由于：S1 + S2 = S3 + S2\x0d所以：(a+2b)(a-2b) = a^2 - 4b^2