First of all, your original query for the "productos" table can be simplified, you don't need the function for this where, just:

$busqueda = DB::table('productos')->where('nombre', 'LIKE', '%'. $term .'%');

For the other related tables, you should do a JOIN (you can read about it on MySQL site), which is basically "mix" two tables into one specifying some conditions, your code can look like this:

$busqueda = DB::table('baterias')->join('marca_baterias', 'baterias.marca_bateria', '=', 'marca_baterias.id')->where('marca_baterias.nombre', 'LIKE', '%'. $term .'%');

And exactly the same for the neumaticos/marca_neumaticos tables.