I recommend cutting on the exact inside of the lines to prevent this.
There's 2 other techniques i can recommend that generally help hide the cut edge. If you are working with thicker papers, no matter how well you have fitted the parts together, the side of the flap-less side usually shows bright white, since u can't print on it. This shows show more pronounced on pictures that are taken with the camera's flash function. (hope is clear what i mean

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I'd read somewhere that using an empty ballpoint pen (or the back of the scalpel) and pre-draw the cutting edges (not the folding edges that's another technique), then cutting them out. This should compress the paper where you cut it, making the cut edge thinner, and thus less visible. Personally I think this one is for those who use scalpels to cut out their paper parts, I'm more comfortable using scissors, and don't really use this. (I have a hard time following the lines exactly with the pen

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The other technique I personally use is this: I have a nice big set of felt markers and colour pencils. After cutting out the part I find the colour closest to the flap-less sides and basically pull the edges over the side of the pen/pencil tips. this usually hides the edges really well.
I use this on almost all my models since Grunt, and in conjunction with my "close fitting skillz"

it really shows. Here are some pointers i got from experience:
-Careful with the felt markers, if u pull them too slow the paper will draw up too much ink, and the edge will get more pronounced
-using color pencils are easier if u sharpen them to a point and use a knife or scissor edge to make a little groove on the side of the tip, after u can pull the edges in this groove and will generally get a better result.
-After using felt markers be sure u don't use too much glue, since its more easily dissolved by the glue than the printer ink (if you're using inkjet ofc.)
-pencils don't leave as pronounced colour as a felt marker, so use them to the more pale colours, and markers for the more saturated ones
-felt markers (at least the ones i use) generally look more dark before drying completely, so I'd advice making a test paper with a dried stroke from all your markers, it's also a big help to match colours, since u can put it next to the piece you want to use the markers on
-I found that if i cant find any decent colors that match, a light grey marker will do wonders. Its not as good as a matching colour, but lightyears better than the bright white of the paper (if the edge is on a really pale coloured part, use a pencil instead)
Hope this helps
