Is the word trouxeram the same in Brazilian and European Portuguese?

Yes

The meaning, spelling, and grammatical function of "trouxeram" (the third-person plural preterite indicative of the verb trazer) are identical in both Brazilian and Continental Portuguese. The difference is purely phonetic. In Brazilian Portuguese, vowels are generally more open and clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," which can make the word sound more consonant-heavy to a Brazilian ear. While the word itself does not change, the surrounding syntax often does (for example, Portuguese speakers almost always use definite articles before possessive pronouns).

Brazilian Portuguese Examples

1. Eles trouxeram o cachorro para brincar. (They brought the dog to play.)
2. Meus amigos trouxeram o lanche no ônibus. (My friends brought the snack on the bus.)
3. Eles trouxeram o celular para a aula. (They brought the cell phone to class.)
4. Meus primos trouxeram presentes de viagem. (My cousins brought gifts from their trip.)
5. Eles trouxeram o suco de laranja. (They brought the orange juice.)

Continental Portuguese Examples

1. Eles trouxeram o cão para brincar. (They brought the dog to play.)
2. Os meus amigos trouxeram o lanche no autocarro. (My friends brought the snack on the bus.)
3. Eles trouxeram o telemóvel para a aula. (They brought the mobile phone to class.)
4. Os meus primos trouxeram presentes de viagem. (My cousins brought gifts from their trip.)
5. Eles trouxeram o sumo de laranja. (They brought the orange juice.)