cube of an even number is
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Step-by-step explanation:
Assume a general even number to be of the form 2n, where n is a whole number (n=0,1,2,3,...). This is true because all even numbers, by definition, are divisible by 2. Now, cube of a general even number= 2n x 2n x 2n = 8n.
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ᴀssᴜᴍᴇ ᴀ ɢᴇɴᴇʀᴀʟ ᴇᴠᴇɴ ɴᴜᴍʙᴇʀ ᴛᴏ ʙᴇ ᴏғ ᴛʜᴇ ғᴏʀᴍ 2ɴ, ᴡʜᴇʀᴇ ɴ ɪs ᴀ ᴡʜᴏʟᴇ ɴᴜᴍʙᴇʀ (ɴ=0,1,2,3,...). ᴛʜɪs ɪs ᴛʀᴜᴇ ʙᴇᴄᴀᴜsᴇ ᴀʟʟ ᴇᴠᴇɴ ɴᴜᴍʙᴇʀs, ʙʏ ᴅᴇғɪɴɪᴛɪᴏɴ, ᴀʀᴇ ᴅɪᴠɪsɪʙʟᴇ ʙʏ 2. ɴᴏᴡ, ᴄᴜʙᴇ ᴏғ ᴀ ɢᴇɴᴇʀᴀʟ ᴇᴠᴇɴ ɴᴜᴍʙᴇʀ= 2ɴ x 2ɴ x 2ɴ = 8ɴ.
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