The Spanish construction "Por mucho / más que + verb" means "No matter how much / However much + verb"; for example:
No matter how much I work I never seem to please my boss.
However much I work I never seem to please my boss.
Por mucho / más que + verb
The verb that follows is generally used in the subjunctive mood, although the indicative can also be used.
Here are some examples:
Por mucho que insista no le voy a dejar entrar.No matter how much he insists I won't let him in.
Por mucho que trabajes nunca conseguirás el ascenso.However much you work you will never get the promotion.
Por más que le explico no se entera.No matter how much I explain it to him he doesn't get it.
No podíamos permitirnos ese coche por mucho que nos gustase.We couldn't afford that car no matter how much we liked it.
As mentioned before, the subjunctive is the preferred mood after this construction, for both hypothetical and real facts. But the indicative can also be used as you can see in the 3rd example above.
In a very similar way we can also use this construction:
Por muy + adjective/adverb + que + verb
In this case, muy is followed by an adjective or an adverb.
Ella está enamoradísima de su novio, por muy feo que sea.She is very much in love with her boyfriend, no matter how ugly he is.
Sus padres los perdonarán, por muy insensatos que hayan sido.Their parents will forgive them, no matter how silly they have been.
Por muy bien que baile, no le darán el primer premio.No matter how well he dances, they won't give him first prize.
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