因式分解 a^3+3(a^2)+3a+b^3+3(b^2)+3b+2

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因式分解 a^3+3(a^2)+3a+b^3+3(b^2)+3b+2

因式分解 a^3+3(a^2)+3a+b^3+3(b^2)+3b+2
因式分解 a^3+3(a^2)+3a+b^3+3(b^2)+3b+2

因式分解 a^3+3(a^2)+3a+b^3+3(b^2)+3b+2
a^3+3(a^2)+3a+b^3+3(b^2)+3b+2 =[a^3+3(a^2)+3a+1]+[b^3+3(b^2)+3b+1] =(a+1)^3+(b+1)^3 =(a+b+2)[(a+1)^2-(a+1)(b+1)+(b+1)^2] =(a+b+2)(a^2+2a+1-ab-a-b-1+b^2+2b+1) =(a+b+2)(a^2+b^2-ab+a+b+1)