This is a bad idea: you want to avoid matrix–matrix products, and only perform matrix–vector products.
Multiplying two m \times m matrices requires \Theta(m^3) operations, while multiplying an m\times m matrix by an m-component vector requires only \Theta(m^2) operations.
This is not specific to Julia—it is a well-known fact in computational linear algebra.
Because the last version computes only matrix–vector products: * is left-associative, so x*B'*A'*A*B*y is equivalent to ((((x*B')*A')*A)*B)*y.