Substitution of expressions for the output

Question

I have a code which gives this kind of output :

W = Sum[v[j]*b[j], {j, 1, 3}];
AA = (v[1]*b[1] + v[2]*b[2] + v[3]*b[3])*2 + 3 ;

I know that if i want to substitute, for example, v[1] with 2 I have to do:

AA = (v[1]*b[1] + v[2]*b[2] + v[3]*b[3])*2 + 3  /. v[1] -> 2

But if i want to substitute the expression of W how should i do? Because if i do this:

    W = Sum[v[j]*b[j], {j, 1, 3}];
AA = (v[1]*b[1] + v[2]*b[2] + v[3]*b[3])*2 + 3  /. 
  W -> (b[1] v[1] + b[2] v[2] + b[3] v[3])

I unfortunately obtain:

3 + 2 (b[1] v[1] + b[2] v[2] + b[3] v[3])

Please help me.

Answer 1

Perhaps this is what you want:

Simplify[AA, W == ww]

3 + 2 ww