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the American dream is the easiest theme to explain in the Great Gatsby come onnnn!
The people in the West Egg (The Buchanans) and the people who live in the East egg (Jay Gatsby, Nick) are all entwined into living this superficial lifestyle. They live life materialistically, the symbolism of the colour green throughout the novel embodies the hope that Gatsby feels. He is living the American dream that with wealth, class and parties he can win over the heart of Daisy. Throwing parties to hide behind the misery he feels.
Gatsby was once a poor man working as a janitor to pay off his student funds. He worked his way into wealth criminally and became rich finally. As part of the 'nouveau riche' he settled down in East Egg in attempt to finally find happiness. Of course he thought happiness would fill him once he was wealthy as that's when he'd have the heart of a certain Daisy Buchanan. But he comes to the realisation that money does not equal happiness and he ends up dying more miserable than he has ever been before.
The Valley of Ashes is the decay of the American Dream. It embodies the realism of the idealistic lifestyle the people in West egg & East egg live. From the outside both their lives look wonderful and colourful, elaborately fashionable. But on the inside, their lives are full of affairs, lies and heartbreak. The Valley of Ashes is described in Chapter 2, grey imagery is used as Nick Carraway states "bleak dust which drift endlessly over it". It is a profoundly depressing area full of the decay of America. Representing the crumbling of the superficial lifes everyone leads. It is prominent as the Valley of Ashes is situated between New york & West Egg & East Egg. Showing it's where all the waste from the parties ends up. Not everything is all about money and glamour.
Sorry that it's so brief- in a little bit of a rush but love explaining this! Hope it helps.