Question

a3+3a2+3a+2的因式分解方法（至少2种方法）

Answer 1

方法一：a^3+3a^2+3a+2=(a^3+2a^2+a)+(a^2+2a+1)+1=a(a^2+2a+1)+(a+1)^2+1=a(a+1)^2)+(a+1)^2+1=(a+1)^2(a+1)+1=（a+1)^3+1=(a+1)(a^2-a+1)
方法二：a^3+3a^2+3a+2=a^3+3a^2+3a+1+1=（a+1)^3+1=(a+1)(a^2-a+1)

Answer 2

a�0�6+3a�0�5+3a+2
=(a�0�6-1)+(3a�0�5+3a+3)
=(a-1)(a�0�5+a+1)+3(a�0�5+a+1)
=(a�0�5+a+1)(a+2)a^3+3a^2+3a+2
=(a^3+2a^2)+(a^2+2a)+(a+2)
=(a+2)(a^2+a+1)

Answer 3

a�0�6+3a�0�5+3a+2=a�0�6+3a�0�5+3a+1+1=(a+1)�0�6+1=(a+1+1)[(a+1)�0�5-(a+1)+1]=(a+2)(a�0�5+a+1) a�0�6+3a�0�5+3a+2=a�0�6+a�0�5+a+2a�0�5+2a+2=a(a�0�5+a+1)+2(a�0�5+a+1)=(a+2)(a�0�5+a+1)