Question

先观察下列各式,你有什么发现:3²=4+5²,5²=12+13,7²=24+25

Answer 1

1.（2n ＋ 1）^2= (2n^2 ＋ 2n)+(2n^2 ＋ 2n ＋ 1)

2.因为(2n^2 ＋ 2n ＋ 1)^2-(2n^2 ＋ 2n)^2

=[(2n^2 ＋ 2n ＋ 1)+(2n^2 ＋ 2n)][(2n^2 ＋ 2n ＋ 1)-(2n^2 ＋ 2n)]

=(4n^2+4n+1)·1

=(2n+1)^2