In a bid to strengthen its mobile business, Google announced on Monday that it would acquire Motorola Mobility Holdings, the cellphone business that was split from Motorola, for $40 a share in cash, or $12.5 billion. The offer — by far Google’s largest ever for an acquisition — is 63 percent above the closing price of Motorola Mobility shares on Friday. Motorola manufactures phones that run on Google’s Android software. Android has become an increasingly important platform for Google, as global smartphone adoption accelerates. The platform, launched in 2007, is now used in more than 150 million devices, with 39 manufacturers.