计算并寻找规律,写出代数式2x4x6x8+16=4x6x8x10+16=6x8x10x12+16=8x10x12x14+16=.

Question

计算并寻找规律,写出代数式 2x4x6x8+16= 4x6x8x10+16= 6x8x10x12+16= 8x10x12x14+16= .

Answer 1

2x4x6x8+16= 400 =20²
4x6x8x10+16= 1936=44²
6x8x10x12+16= 5776=76²
8x10x12x14+16= 116²
……
实际上得到的规律就是
2a*(2a+2)*(2a+4)*(2a+6)
=16*a*(a+1)*(a+2)*(a+3)+16
=16*[a*(a+1)*(a+2)*(a+3)+1]
=16*[(a²+3a)*(a²+3a+2)+1]
=16*[(a²+3a)²+2(a²+3a)+1]
=(4a²+12a+4)²