How Do I Normalize a Three Qbit State?

[pleasehelpmeno]

Homework Statement

I have a three qbit state:
$(a|00> + b|11>)\bigotimes(c|0>+d|1>)$
and I need to normalise it, I realize that I could deconstruct it into matrices and work it though and solve it but there must be a more efficient way.

Homework Equations

The Attempt at a Solution

I am unsure really how to proceed from here, I kow that to normalise one does $<\psi|\psi>=1$ but I am confused because this is a 3 qbit state, would it simply be $ac(ac)^{*} + ad(da)^{*} + bc(cb)^{*} + bd(db)^{*}=1$?.

 

[Oxvillian]

would it simply be $ac(ac)^{*} + ad(da)^{*} + bc(cb)^{*} + bd(db)^{*}=1$?.

Looks right to me

You just multiply together the inner products from the two spaces.