a+b+c+d=0 
=>a+b = - (c+d) 
=> (a+b)^3= - (c+d)^3 
=> a^3 + b^3 + 3ab(a+b) = - c^3 - d^3 - 3cd(c+d) 
=> a^3 + b^3 + c^3 + d^3 = - 3ab(a+b) - 3cd(c+d) 
=> a^3 + b^3 + c^3 + d^3 = 3ab(c+d) - 3cd(c+d) ( Vì a+b = - (c+d)) 
==> a^3 + b^3 + c^3 + d^3 = 3(c+d)(ab-cd) (đpcm).

ta có a+b+c+d = 0=> b+c= -( a+d) => (b+c)^3 = - (a+d)^3

=> b^3+ c^3 + 3bc( b+c) = -( a^3 +d^3 + 3ad(a+d))

=> a^3+b^3+c^3+d^3 = - 3ad( a+d) - 3bc(b+c) = 3ad(b+c) - 3bc(b+c) 

= 3(b+c)(ad-bc)

sao cậu tự đặt câu hỏi rồi lại tự trả lời luôn         

       thế là sao??????????

minh thich la minh lam thoi

a+b+c+d=0

=>a+d=-(b+c)

=>(a+d)^3=-(b+c)^3

=>\(a^3+d^3+3ad\left(a+d\right)=-b^3-c^3-3bc\left(b+c\right)\)

=>\(a^3+d^3+3ad\left(a+d\right)=-b^3-c^3+3bc\left(a+d\right)\)

=>\(a^3+d^3+b^3+c^3=3bc\left(a+d\right)-3ad\left(a+d\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3\left(a+d\right)\left(bc-ad\right)\)

=>\(a^3+b^3+c^3+d^3=3\left(b+c\right)\left(ad-bc\right)\)

Ta có: a+b+c+d=0

\(\Leftrightarrow b+c=-\left(a+d\right)\)

\(\Leftrightarrow\left(b+c\right)^3=-\left(a+d\right)^3\)

\(\Leftrightarrow b^3+c^3+3bc\left(b+c\right)=-\left[a^3+d^3+3ad\left(a+d\right)\right]\)

\(\Leftrightarrow b^3+c^3+3bc\left(b+c\right)=-a^3-d^3-3ad\left(a+d\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=-3bc\left(b+c\right)-3ad\left(a+d\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=-3bc\left(b+c\right)-3ad\cdot\left[-\left(b+c\right)\right]\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=-3bc\left(b+c\right)+3ad\left(b+c\right)\)

\(\Leftrightarrow a^3+b^3+c^3+d^3=3\left(b+c\right)\left(ad-bc\right)\)(đpcm)