I'm searching for exercises for practising operations with terms. They should involve
- working with decimal numbers and fractions (ideally one should convert decimal numbers to simple fractions like halves, fourths or fifths to simplify calculations and be able to cancel out factors)
- expanding products and getting rid of parenthesis, in particular deal with plus and minus signs and possibly use binomial formulas
- using power laws
- combining terms
and ideally give a possibly simple result. An example of what I have in mind would be something along the lines of
$$1.25(6a-4b)^2(0.4a^2b)^2 - 2.2(5a-4b)(4a-5b)(0.5ab^2)(2.5a^3b)$$
(however, this example doesn't simplify well at all and gives many terms with ugly coefficients).
Hints on how to design such problems myself or even automatize the generation of such problems with a little program are also welcome!
Thanks for any input!