Want to make a banner combining these two images. Clearly the image on the left has a different background (in a square) to the one on the right which I am trying to get rid of and make it look natural. To make it seem like it is one image with the same background. I do not know the quickest/most efficient way in doing this. Any help would be fantastic.
Put both images in a different layer at each side of the banner document
Pick the background color of the second layer and Fill it > Mode Behind
Make a rectangular selection from top to bottom at the right side of the top layer and scale it horizontally to the right:
To this selection, Menu Effect > Noise > Median
Apply a Mask to this layer
Use the Gradient Tool to fade the mask from right to left, from black to white
Images seem to be single layer ones, there's no easy to replace background layers. Simple color matching do not work because the background lightning is non-uniform, you can make only small areas of backgrounds to match by using Image > Adjustments > Match Color. (tested)
You have 3 options left:
Bite the bullet and remove the background from one of the images - the right image seems easier. Then you must put a new backround layer and fix the shadows.
Place the images so that there's a reasonably short seam and put a smooth transition zone between the images. That idea is already proposed in another answer.
Place a third element which covers the seam.
Option 1 is tried here. The selection is made only with the magic wand. The 2nd image area was copied to another layer to keep it safe. The shadows aren't fixed, their edges are no more smooth.
Magic wand selection can be enough in a low res web image, but printing needs a clipping path or a very careful deletion with polygonal lasso selections.
A new background was added. It's a gradient. The edges of the 2nd image were faded with the eraser in low opacity mode. A missing corner is added with the cloning brush.
The 2nd option is already presented.
The 3rd option is difficult. The covering element very easily catches too much attention: