Blog 1- Searching for Patterns in Mathematics Mathematics is about finding and collecting the existing patterns from what we have learned or in our daily lives, then combining all materials to summarize as a definition, a theorem or even a formula. We can start with a simple expansion below. (a + b) (a – b) = (a + b)a – (a + b)b = aa + ba – ab – bb = a 2 – b 2 Now, we want to substitute 1 and x for a and b, respectively, we have (1 + x) (1 – x) = 1 – x 2 Now let’s replace (1 + x) in (1 + x)(1 – x) with (1 + x + x 2 ), we obtain that (1 + x + x 2 ) (1 – x) = (1 + x + x 2 )1 – (1 + x + x 2 )x = 1 + x + x 2 – (x + x 2 + x 3 ) ...