“表明” is a verb. It means someone indicate his/her attitude ，point and suggestion. You could use some nouns as its object, such as “立场，意见，看法，观点” etc. Ex. , 他表明了他的立场。这件事表明了大众的看法。 “表情” is a noun. It means the feelings express on a person's face. It should not be used as a verb or other categories of words. “表示” can be used as a verb or a noun. When it is a verb, it means someone show his/her attitude , feeling and emotion. It can replace “表明” in a few situation. Be carefully, The subject of “表示” is human , human group or some intelligent things. Ex. 他表示很开心。 学校领导表示愿意和企业合作。 When it is a noun （usually in oral Mandarin）, it means someone should do something or show his attitude to someone. It is hard to express in language. Ex. 她问他的男朋友：明天我生日，你有什么表示？ “表现” is a verb or a noun. It means someone show his/her thought or advantages. You could use some nouns as its object, such as “犹豫，果断，优点” etc. Ex.， 对于这件事，他表现的很果断。 那个员工很想快点表现自己的优点。 When it is a noun, it means someone's performance in an event. Ex., 他在这份工作上的表现很好。 “表演”is a verb or a noun. When it used as a verb. It means someone perform an act of play, music or some kinds of entertainment. Ex. 那个明星表演了一支舞蹈。 韦德在比赛中表演了灌篮。 When it is a noun, it means an act or a show. Sometimes it is a metaphor that means someone's action in an event . Ex. 那个歌手的表演相当精彩。 他在这件事过程中的表演实在让人看不透。 Hope it could help.

“表明”我会用show来解释，动词，就是展示事物的某些特性；也有阐述观点的意思，如“表明想法”。 “表现”，一做动词，意为展现，如“表现得很慌张”；二做名词，表示事物呈现的状态，如“他的表现”。 “表演”就是perform。 “表情”一般特指面部呈现的样子。 “表示”，一，动词，阐述观点，如“表示不同意”；二，动词，有代表意义，或等量，如“一厘米表示十毫米”，“刻度计的指针到达这个位置表示水已注满”；三，做名词，口语用，如“他是什么表示？”（等于“他表示什么样的态度？”）

表明: show Sentence: Franklin's experiments showed(表明) that the lightning is an electrical discharge. 表情: facial expression 表示: express/ show （familiar with 表明） Sentence: She expressed her sympathy to the bereaved family. 表现: performance, Someone's or something's performance is how successful they are or how well they do something Sentence: That study looked at the performance of 18 surgeons. 表演: A performance involves entertaining an audience by doing something such as singing, dancing, or acting Sentence: her performance as the betrayed Medea.

表情：一般我们说面部表情 facial expression 表演：一般我们可以说演出，但是演出更加的大型或正式一些。show or performance 表示：1.显示某种意义. 2.用语言、行动显出某种思想、感情、态度。如：表示遗憾，表示感谢。 表明：表示自己对某种事情的观点、态度并陈述自己的一些思想、感情。如：表明立场。 表现 ：显露出来，后多接事物的现象，如：表现得很勇敢，良好表现。