Why is it so hard to learn the HP prime g2?

[Albert Chan]

(08-15-2023 08:32 AM)Nigel (UK) Wrote:  Once you’ve worked out (sqrt(x-9))^8 and got (x-9)^4, the next step is not Simplify, but Expand.

CAS> expand((1+x)^4 - (1-x)^4)

x^4 - (-x)^4 + 4*x^3 - 4*(-x)^3 + 6*x^2 - 6*(-x)^2 + 8*x

CAS> simplify(Ans

8*x^3 + 8*x

I wish CAS expand produce terms without (-x)^n.
I think this should be fixed ... until then, I'll use simplify.

---

Example, from book Algebraic Inequalities, old and new methods

Warm-Up exercise 3:
Positive (a,b,c), prove (a+b+c)^5 ≥ 81 * a*b*c * (a^2+b^2+c^2)

CAS> f := (a+b+c)^5 - 81 * a*b*c * (a^2+b^2+c^2)
CAS> member("-", str(simplify(f(b=a+x, c =a+x+y

0      // "-" not found

With symmetry, we can assume (a,b,c) sorted, 0 < a ≤ b ≤ c
--> f, in terms of (a, x=b-a, y=c-b), does not have negative terms.
--> f ≥ 0      QED