> ... using a less strict version... Nice to know there's a name for it.

Using distributivity for creative simplification of a hard multiplication problem is a useful skill... It's a mental shortcut, like Russian Peasant Multiplication.

But it isn't the same as, or just a "less strict" version of it. The latter is an algorithm, and relies on binary arithmetic and the "simple" operations of doubling, halving, and summation.