How to Say "demonstrate" in Spanish
The most common Spanish word for “demonstrate” is “muestre” — use 'muestre' when you want to show someone how something operates or functions, like giving a demonstration of a product..
muestre
/MWES-treh//ˈmwestɾe/

Examples
Por favor, muestre su identificación.
Please, show your identification.
Espero que la empresa muestre mejores resultados.
I hope the company shows better results.
No creo que él me muestre la verdad.
I don't believe he will show me the truth.
The 'O' to 'UE' Change
This word comes from 'mostrar'. In many forms, the 'o' changes to 'ue' when it is the part of the word we emphasize most while speaking.
Using 'Muestre' for Commands
Use 'muestre' when you are politely telling someone (using 'usted') to show you something, like a ticket or a passport.
Don't Forget the 'UE'
Mistake: “Espero que él mostre el camino.”
Correction: Say 'muestre' instead. Many people forget that the 'o' in 'mostrar' must change to 'ue' in this form.
probar
proh-BAHR/pɾoˈβaɾ/

Examples
Necesitas documentos para probar tu edad.
You need documents to prove your age.
El científico no pudo probar su hipótesis con los datos.
The scientist could not prove his hypothesis with the data.
Su comportamiento prueba que está equivocado.
His behavior proves that he is wrong.
Usage with 'Que'
When 'probar' introduces a statement of fact, it is usually followed by 'que' and the simple verb form (indicative): 'El reporte prueba que funciona' (The report proves that it works).
Showing vs. Proving
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