godin

This stuff is very effective, but I'd only use a tiny amount, and only if the wood is sealed with varnish: https://www.desolvit.co.uk/product/de%E2%80%90solv%E2%80%90it-sticky-stuff-remover/

We call it "multiplying out brackets" or "expanding brackets". By the way, there's a difference between: (a + b) (c + d) and: (ax + b) (cx + d) In the first case, when a, b, c and d are all constant values, I think we'd normally simplify them to a single constant. The second case is more similar to your original example: (6x + 7) (x + 4) Here x is not a constant, and there are two factors, each containing a constant plus a multiple of x: 6x + 7 x + 4 I'd guess we could take the coefficients of these binomials as vectors and use matrix multiplication. If you're interested to work that out, look up "linear algebra".

Don't know why you're calling yourself dim. I've not thought about this before (which is dim) I'd guess the reason we've got several ways to write multiplication is to avoid confusion between symbols: x and × . and · By convention multiplication is implicit, and the other notations are used to avoid ambiguity. Eg. "2πr" is equivalent to 2 times π times r, but if we use 3.14 as an approximation of π, then it would be harder to read in these notations: 2 3.14r 2·3.14r It easy to make mistakes in those cases if the spacing isn't clear. To make it clearer we can write something like: 2 × 3.14r 2(3.14r) 2 × 3.14 × r Which notation you use probably depends on what area you're working in, and I think conventions have changed over time. There are some situations where there is more than one kind or multiplication, eg cross product and dot product when working with vectors. There are also situations where only allowing implicit multiplication and using parentheses would be confusing if it conflicted with notation to denote function.