believe in: 相信
Do you believe in Maxism?
你信仰马克思主义吗？（信仰）

involve in: 牵涉
A late booking may involve you in extra cost.
预订晚了的话你可能要额外多花钱。
In view of the large amount involve in this transaction, we hope you'll agree to our request for installment payment.

鉴于这笔交易数额较大，希望贵方能同意分期付款。

blue in the face: 脸上发紫（恼怒）
He was blue in the face, ie His face was a purplish colour because of cold or exertion.

他脸色发青（因寒冷或用力过度而稍泛紫色）.
He was blue in the face with cold.
他冷得脸上发青。