Is There Symmetry in the Signs of Newton's Identities?

[Jhenrique]

Look this relationship:

http://en.wikipedia.org/wiki/Newton's_identities#Related_identities

If I isolate the variable p, I'll have:

$p_1 = 1h_1$
$p_2 = 2h_2-h_1p_1$
$p_3 = 3h_3-h_2p_1-h_1p_2$

So, my question is: BTW, would be true that:

$p_1 = 1h_1$
$p_2 = 2h_2+h_1p_1$
$p_3 = 3h_3+h_2p_1+h_1p_2$

?

EDIT: I'm asking because with base in other formulas seems that there is some symmetry between the signals...

 

[Mark44]

If I isolate the variable p, I'll have:

$p_1 = 1h_1$
$p_2 = 2h_2-h_1p_1$
$p_3 = 3h_3-h_2p_1-h_1p_2$

So, my question is: BTW, would be true that:

$p_1 = 1h_1$
$p_2 = 2h_2+h_1p_1$
$p_3 = 3h_3+h_2p_1+h_1p_2$

No.
The first equation just above is correct, but the next two aren't. You can' t just change the sign arbitrarily.
If $p_2 = 2h_2-h_1p_1$, you can replace $p_1$ by $h_1$ to get
$p_2 = 2h_2 - h_1^2$