I am thinking of purchasing an additional 2 sticks of 16GB RAM for the P51.

I understood that the 8GB that comes by default with the P51 is mounted under the keyboard.

Question 1: Can I have a 40GB configuration? (with the 8GB mounted under the keyboard, and the two additional sticks mounted in the slots to be found underneath the laptop). Yes, I know, I will be taking a speed hit on the 8GB stick of about 15% speed loss.

Question 2: If the answer to Question 1 is yes, then where should the 8GB stick ideally be located? I am thinking to have the laptop use firstly the 32 GB of RAM from the two bought sticks, and only if it runs out of RAM on those, to use the 8GB (which would be better than swapping on HDD).

Thanks!

The answer to the first question is yes, and I believe the memory is configured dynamically and "it" decides how to use the space.  I think the 15% figure is more theoretical than actual.  I doubt you would find anything you would notice.

If you're wanting to use the new 2x16GB memory "first" because it is faster than the Lenovo-installed 1x8GB of memory, that isn't going to be of any advantage even if it were to happen.  With memory at different speeds, the BIOS will re-time them so that they all run at the slowest speed... of the slowest memory.

Given this common slowest speed, and running in single-channel mode because of the 1x8GB under the keyboard, you will simply be operating as 40GB in single-channel mode at the slowest memory speed present.

That's why ideally memory is installed in 2x "kits", as matched pairs in the one or two pairs of memory sockets (i.e. either two or four sticks of memory) all of which have identical timings.  That way you get dual-channel mode at the one-and-only speed of all the memory you bought, from all of the two or four sticks of memory you installed.

No, I was thinking that memory banks come in pairs. 1 and 2. 3 and 4. 

I was thinking of purchasing same speed 16GB sticks as the 8 GB stick. However, if my entire system will be single-channel (including banks 3 and 4) just because slot 2 is unnocupied, then I guess I will just have to take the 8 GB out.

Personally, I thought that the controller is smart enough to operate banks 3 and 4 in dual channel mode, and bank 1 in single channel mode.

To really answer the question, we'd need to know how the BIOS and memory controller on the motherboard actually works. I don't know where we'd find the Lenovo documentation which would discuss this.

Also, just for clarity, the two "overlaid" dual-channel A2/B2 memory sockets under the keyboard are technically identified as #1 and #3 (if you get only one memory stick from Lenovo it will be placed in #3, A2, which is the top socket of the overlaid pair), with the other two dual-channel A1/B1 memory sockets on the underside of the laptop are technically identified as #2 and #4.

However apparently it IS possible to get the hybrid performance you hypothesized could be provided, with a mix of single-channel and dual-channel performance, if you opt out of the recommended approach of always installing identical size/timing memory cards in A1/B1 and/or A2/B2.  But it does depend on the hardware and motherboard vendor as to whether or not that's possible.

For example, I have an ASUS Z170 Deluxe (Skylake) motherboard in my homebuilt desktop PC.  Its alternating color-coded two pairs of two memory sockets are physically identified as A1/A2 and B1/B2.  Optimally you're supposed to populate them with the same size/timing memory cards in A1/B1 (which are both black) and A2/B2 (which are both blue), same as with Lenovo's #3/#1 and #4/#2.

But the owner's manual for the motherboard specifically says: "You may install varying memory sizes in Channel A and Channel B.  The system maps the total size of the lower-sized channel for the dual-channel configuration.  Any excess memory from the higher-sized channel is then mapped for single-channel operation."

Now I don't know if Lenovo's laptop motherboard works the same as the ASUS desktop motherboard but if it did then I would expect it to behave as follows:

(a) Under-the-keyboard:  1x8GB in A2

(b) Under-the-laptop:  2x16GB in A1/B1

(c) total size of channel A:  8GB+16GB=24GB

(d) total size of channel B: 16GB

==> lower sized channel is B, so 16GB would operate as dual-channel (on A and B) and the remaining 8GB on channel A would operate as single-channel (on A).

At least that's how it would work on my ASUS Z170 Deluxe if I only populated three sockets as above... which, personally, I would never do.  The only justification would be (a) to avoid removing the keyboard in order to add your own second 1x8GB memory card under the keyboard to complete that matched pair as well as adding your own 2x16GB under the laptop to increase total memory size and also obtain optimal dual-channel performance for 100% of the memory, or (b) to avoid buying and paying the price for a 2x16GB memory configuration from Lenovo, which is the only option to get two matched memory cards factory installed under the keyboard to obtain dual-channel mode for 100% of that memory.