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Hi

Could you please tell me the difference, if any?

She is doing her laundry.

She is doing the washing up.

Thanks,

Tom
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It's not very natural.

She's doing the laundry. She's doing the dishes. She's cleaning the bathroom. All of those involve washing of some sort. I would wonder which you mean.

In times past, you might see "the washing" to mean the laundry, but at least in the US, it's not used alone.
Comments  
Mr. TomShe is doing her laundry.
She is washing her dirty clothes.
Mr. TomShe is doing the washing up.
She is washing the dirty dishes after a meal.

CJ
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Many thanks, CJ.

Is there an expression:

She is doing the washing.

(if yes, what is the meaning?)

Thanks,

Tom
 BarbaraPA's reply was promoted to an answer.