因式分解a^3+3a^2+3a+1

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因式分解a^3+3a^2+3a+1
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因式分解a^3+3a^2+3a+1
因式分解a^3+3a^2+3a+1

因式分解a^3+3a^2+3a+1
a^3+3a^2+3a+1
=(a+1)³

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

a^3+3a^2+3a+1
=(a^3+1)+3a(a+1)
=(a+1)(a^2-a+1)+3a(a+1)
=(a+1)(a^2-a+1+3a)
=(a+1)(a+1)^2
=(a+1)^3