Question

What is the formula of Binomial Theorem ?​

Answer 1

The Binomial Theorem states that, where n is a positive integer: (a + b)n = an + (nC1)an-1b + (nC2)an-2b2 + … + (nCn-1)abn-1 + b.

Answer 2

ᴛʜᴇ ʙɪɴᴏᴍɪᴀʟ ᴇxᴘᴀɴsɪᴏɴs ғᴏʀᴍᴜʟᴀs ᴀʀᴇ ᴜsᴇᴅ ᴛᴏ ɪᴅᴇɴᴛɪғʏ ᴘʀᴏʙᴀʙɪʟɪᴛɪᴇs ғᴏʀ ʙɪɴᴏᴍɪᴀʟ ᴇᴠᴇɴᴛs (ᴛʜᴀᴛ ʜᴀᴠᴇ ᴛᴡᴏ ᴏᴘᴛɪᴏɴs, ʟɪᴋᴇ ʜᴇᴀᴅs ᴏʀ ᴛᴀɪʟs). ᴀ ʙɪɴᴏᴍɪᴀʟ ᴅɪsᴛʀɪʙᴜᴛɪᴏɴ ɪs ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴏғ sᴏᴍᴇᴛʜɪɴɢ ʜᴀᴘᴘᴇɴɪɴɢ ɪɴ ᴀɴ ᴇᴠᴇɴᴛ. ᴛʜᴇ ʙɪɴᴏᴍɪᴀʟ ᴛʜᴇᴏʀᴇᴍ ᴡɪᴅᴇʟʏ ᴜsᴇᴅ ɪɴ sᴛᴀᴛɪsᴛɪᴄs ɪs sɪᴍᴘʟʏ ᴀ ғᴏʀᴍᴜʟᴀ ᴀs ʙᴇʟᴏᴡ :

${ \boxed{ \underline{\underline{\mathfrak{\red{ (x + ᴀ) ɴ = ∑ ᴋ = 0 ɴ (ᴋ ɴ) x ᴋ ᴀ ɴ − ᴋ }}}}}}$