# 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 $$z$$.

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