帮 and 帮忙
bāng and bāngmáng

1. 帮 has two meanings:
1) to support someone materially or spiritually, or actually do a part of the work for them; and,
2) when someone is doing something such as hourly or informal labor.

In the first usage, 帮 usually takes a direct object (the person) and an indirect object (doing something).
(1) 他帮我把行李运回来了。
(2) 他父母帮他物色了一个对象。

2. 帮忙 is verb-object phrase, meaning "actual help, or actual support to another person who needs help."
(1) 能请你帮个忙吗？
(2) 你今天可算是帮了我一个大忙了。
(3) 请帮忙把碗筷收拾一下吧。

帮倒忙 means "when trying to help somebody, intentionally or unintentionally, one makes a lot of trouble." 越帮越忙 (the more help, the more troublesome) has a similar meaning.

帮 and 帮忙 are not interchangeable.

1.“帮”有两个意思，(1) 当某人做某事时，在精神、物质上给予支持，或实际参与一部分工作。(2) 指从事体力雇佣劳动，如“帮工”，“帮短工”等。第一个意思中，“帮”常带直接宾语（指人）和间接宾语（指从事的某事）。
2.“帮忙”在结构上是动宾关系，意思上表示具体的帮助，或表示别人有具体困难或需要劳力时给予支持。
“帮倒忙”表示帮助别人时，有意无意反倒给别人增添了麻烦。“越帮越忙”也有类似意思。
“帮”与“帮忙”一般不能互换。