Collect simplifies the task of factoring similar terms in a large expression by gathering them
to one side. The subject provides a template that is matched against additive and multiplicative
operands. An operand that contains a matching subexpression is commuted to the left.
For example, x^3-1 transforms to x^3-2⋅x^2+x-x^2+2⋅x-1
after distribution and simplification. Them terms in x^2 are
commuted to the left by selecting x^3-2⋅.{x^2}+x-x^2+2⋅x-1 or
x^3-2⋅x^2+x-.{x^2}+2⋅x-1 and Collect . With either
subject, the result is -(2⋅x^2)-x^2+x^3+x+2⋅x-1. Then the first
two terms can be selected, factored and simplified to -3⋅x^2+x^3+x+2⋅x-1.
Similarly, x^4-2⋅x^2+1 factors to (x-1)⋅(x+1)⋅(x-1)⋅(x+1).
With the selection (.{x-1})⋅(x+1)⋅(x-1)⋅(x+1), Collect produces (x-1)⋅(x-1)⋅(x+1)⋅(x+1) which can be factored and simplified
to (x-1)^2⋅(x+1)^2.
