# Let's create an identity

Algebra Level 5

\begin{aligned} 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{aligned}

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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