Step-by-step explanation:
This is an application of the distributive property. (It is also a variation on the way you were taught to do multiplication by hand.)
684 × 7 = (600 +80 +4) × 7
= (600 × 7) +(80 × 7) + (4 × 7)
= 4,200 + 560 + 28
= 4788
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