Let's create an identity
Algebra
Level
5
\[ \begin{eqnarray} w &=& { a }^{ 4 }+{ b }^{ 4 }+{ c }^{ 4 }+{ d }^{ 4 } \\ x &=& { a }^{ 2 }+b^{ 2 }+{ c }^{ 2 }+{ d }^{ 2 } \\ y &=& ab+ac+ad+bc+bd+cd \\ z &=& abcd \\ \end{eqnarray} \]
Let \(a,b,c\) and \(d\) be real numbers; and \(w,x,y\) and \(z\) some unknown constants such that they satisfy the system of equations above. State the following expression
\[(a+b+c+d)({ a }^{ 3 }+{ b }^{ 3 }+{ c }^{ 3 }+{ d }^{ 3 }+abc+abd+bcd+acd) \]
in terms of \(w,x,y\) and \(z\).
by
Inderjeet Nair