Question

1.任意两个连续奇数的平方差有什么特点?

Answer 1

(2n+1)^2-(2n-1)^2

=(2n+1+2n-1)(2n+1-2n+1)

=8n

10^2-9^2+8^2-7^2.+2^2-1^2

=(10+9)(10-9)+(8+7)(8-7)+……+(2+1)(2-1)

=19+15+11+7+3

=(19+3)+(15+7)+11

=11*5

=55

(5-y)(-y-5)-(2y+1)(2y-1)

=(y-5)(y+5)-(2y+1)(2y-1)

=y^2-25-(4y^2-1)

=-3y^2-24