Classifying XOR dataset with a single perceptron

Hi, I recently watched your video on [multilayered perceptrons](https://www.youtube.com/watch?v=u5GAVdLQyIg) and I had the following question:

**Instead of adding new neurons to classify a non-"linear separable" problem (e.g. XOR), can we instead add more inputs ?**

If we go back to your previous video about [perceptrons](https://www.youtube.com/watch?v=ntKn5TPHHAk), your inputs are the coordinates `x` and `y` of a point. If we add the `x.y`, being the multiplication of the two coordinates, wouldn't this be enough to replace the use of "NAND" and "OR" neurons you use in your example ? Tensorflow's [playground](https://playground.tensorflow.org/#activation=tanh&batchSize=10&dataset=xor®Dataset=reg-plane&learningRate=0.03®ularizationRate=0&noise=0&networkShape=&seed=0.42727&showTestData=false&discretize=false&percTrainData=50&x=true&y=true&xTimesY=true&xSquared=false&ySquared=false&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false) is a nice tool to visualize the effect of adding new inputs, layers, nodes etc... to a classification problem.

This brings me to the real questions:

**What is the right way of building a NN ? What's the closest we can get to a universal NN ?**