Brazo means arm, and broma means joke. Those are 2 very common words on their own. They are also commonly used in Spanish idioms and expressions. I’d like to teach you a few Spanish expressions involving bromas and brazos:

no dar su brazo a torcer | not to let someone twist one’s arm, not to give in, to hold one’s ground

Ejemplos:
A pesar de todas las amenazas, no dio su brazo a torcer.
(In spite of all the threats, he stood his ground.)
Esperamos que no dé su brazo a torcer.
(We hope that he doesn’t give in.)

luchar a brazo partido | to fight bitterly, to fight tooth and nail, to go at it hammer and tongs

Ejemplos:
Los soldados lucharon a brazo partido contra sus enemigos.
(The soldiers fought tooth and nail against their enemies.)
A pesar de sus lesiones, Ana luchó a brazo partido.
(In spite of her injuries, Ana gave all that she had.)

quedarse con los brazos cruzados | to sit back and do nothing, to sit on one’s hands

Ejemplos:
Se enojó y se quedó con los brazos cruzados.
(He got angry and did nothing.)
Debido a su flojera, Roberto suele quedarse con los brazos cruzados.
(Because of his laziness, Robert usually sits back and does nothing.)

no estar para bromas | to be in no mood for jokes/laughter

Ejemplos:
Debido a la muerte de su madre, Juán no esta para bromas.
(Because of the death of his mother, Juán isn’t in the mood for joking around.)
José no esta para bromas porque tiene mucha tarea.
(José isn’t in a joking mood because he has a lot of homework.)

estar de bromas | to be in a joking mood

Ejemplos:
Nelson siempre esta de bromas.
(Nelson is always in a joking mood.)
Suelo estar de bromas.
(I’m usually in a joking mood.)

entre bromas y veras | half-jokingly and half seriously

Ejemplos:
Lo dijeron entre bromas y veras.
(They said it kind of half-jokingly, half-seriously.)
Es difícil entender porque habla entre bromas y veras.
(He is difficult to understand because he speaks half-jokingly.)