Question

m(m+1)(m+2)(m+3)+1?用因式分解

Answer 1

（m+1)（m+2)(m+3)(m+4)+1 第一项与第四项相乘，第二项与第三项相乘得： =(m²+5m+4)(m²+5m+6)+1 =(m²+5m+4)²+2(m²+5m+4)+1 =(m²+5m+4+1)² =(m²+5m+5)²

Answer 2

m(m+1)(m+2)(m+3)+1
=(m^2+3m) (m^2+ 3m +2) +1
= (m^2+ 3m)^2 + 2(m^2+ 3m) +1
=(m^2+3m+1)^2