x*x*x*x+2x*x*x+3x*x-2x+1因式分解x*x*x*x+2x*x*x+3x*x+2x+1原式=a^4+2a^3+3a^2+2a+1=(a²+a+1)²怎么推出这结果a^4+2a^3+3a^2+2a+1=a^4+2a^3+a^2+2a^2+2a+1=a^2(a^2+2a+1)+2a(a+1)+1=a^2(a+1)^2+2a(a+1)+1=[a(a+1)+1]^2=(a^2+a+1)

Question

x*x*x*x+2x*x*x+3x*x-2x+1 因式分解 x*x*x*x+2x*x*x+3x*x+2x+1 原式=a^4+2a^3+3a^2+2a+1=(a²+a+1)² 怎么推出这结果
a^4+2a^3+3a^2+2a+1
=a^4+2a^3+a^2+2a^2+2a+1
=a^2(a^2+2a+1)+2a(a+1)+1
=a^2(a+1)^2+2a(a+1)+1
=[a(a+1)+1]^2
=(a^2+a+1)^2

Answer 1

x*x*x*x+2x*x*x+3x*x+2x+1
=x^4+2x^3+x²+2x²+2x+1
=x²(x+1)²+2x(x+1)+1
=(x(x+1)+1)²
=(x²+x+1)²