已知a+b=1,求a^3+3ab+b^3的值

a^3+3ab+b^3
=(a^3+b^3)+3ab
=(a+b)(a^2-ab+b^2)+3ab
=1*(a^2-ab+b^2)+3ab
=a^2+2ab+b^2
=(a+b)^2
=1^2
=1.

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

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

因为(a+b)^3=a^3+3ab(a+b)+b^3

又知a+b=1

So.........

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

a^3+3ab+b^3
=(a+b)^3-3a^2b-3ab^2+3ab(变形根据下面公式,应该知道的!)
=1-3ab(a+b-1)
=1-0
=1

公式(a+b)^3=a^3+3a^2b+3ab^2+b^3