@end of nights,
With regard to the tenth bit (term):
A = 1 (given)
Since A^C^D = 0, C or D (but not both) is 1.
Since A^B^C^D = 1, B must be 1. That results in three 1s and one 0.
"...since there are at least two 1s, which would make it a 0."
The result is 0 when there are an even number of 1s. Three ones would make it a 1.
xor is commutative and associative, so you can move or remove your parentheses as you like. You can also rearrange the terms any way you like.