I am looking for books that encourage creative problem-solving at the high school level. I attended secondary school in the United States and I have noticed that there are techniques that I was not taught thoroughly.
Please suggest books that address the following:
- Substitution/change of variable for single variable equations
- Factoring non-algebraic expressions
- "smart" manipulation of expressions
I have listed YouTube videos depicting the kinds of problems I would like to be able to solve. The videos are in Russian, but they all involve solving equations.
I am aware of The Art of Problem Solving but I feel it addresses contest math.