-a³-100a,

Factor out -a

-a(a²+100)

That' as far as it will factor. [you can factor the difference 
of two squares but you can't factor the sum of two squares)

----------------------
Second problem:

-4w^3-16w^2+20w

factor out -4w

-4w(w²+4w-5)

Now you can factor the trinomial:

-4(w+5)(w-1)

-------------------------

Note that if the first one had been

-a³+100a

then you'd factor out

-a(a²-100)

then you could factor the difference of two squares as

-a(a-10)(a+10)

But if the sign of both terms is -, the way I showed at the
top is the only way to factor it.

Edwin