You're cleaning the kitchen. Your wife isn't helping you. You want to ask her to help, but you'd like to ask politely so that you don't start a fight. You ask this.
Baby, would you mind giving me a hand with this?
Words like "baby", "sweetheart", "darling", and "dear" are sometimes used between couples in place of each other's names. These words are called "terms of affection". It can sound more sweet and loving to use these words than to call someone by name.
"Would you mind ___ing?" is a good way to politely ask for something that isn't too much trouble for the other person. Some more examples:
Would you mind passing me that bottle over there?
Would you mind watching my bag for a few minutes?
Would you mind sending me a list of everyone who's coming?
"Give (someone) a hand" means to help someone. The word "help" has a wide meaning. It can be used to describe helping someone with a small problem, or with a serious emergency. So when you're asking for help, it's important to express how serious the problem is. For big emergencies, you just yell:
For smaller but still serious problems, you can ask:
Can you help me?
And for small problems that aren't an emergency, you ask:
Can you give me a hand?
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