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Expressions

An expression is just a string of numbers and/or variables, with no equal sign in sight. Part of the reason some people get so freaked out by algebra is that they may see an expression like this:

3x + y2

...and assume that they’re looking at some foreign language. What are numbers and letters doing, jumbled together like some sort of keyboard free-for-all? And what is that little "2" doing floating up there near the top? What is it, filled with helium?

Once you understand what these numbers and symbols mean, though, everything becomes easier to handle. For example, say you have a vegetable garden with 3 tomato plants. You high roller, you. How many tomatoes are there on each plant? That’s what x stands for. Suppose that you also went through the garden and sprinkled onion seeds in a square plot, with the same number of onions in each row and column. That’s what the y stands for, so there are y × y = y2 onions in that square of dirt.

If we're told that each tomato plant yields 4 tomatoes, we know that x = 4 and that there are 12 total tomatoes in your garden (3 × 4 = 12). Then we find out that 3 onion seeds were planted in each row and column, so that's 32 = 9 total onions. How many total veggies are in our garden?

Just plug everything we know into our original expression:

3x + y2
3(4) + 32
12 + 9 = 21 veggies

Meanwhile, you're sitting there and chowing down on that Big Mac while we're counting all the produce in your garden. How ironic.

Algebra is simply a way of abbreviating real-life scenarios—think of it as a type of shorthand for dealing with calculations that can get much more complicated than tallying up tomatoes and onions. Unless you're allergic to tomatoes, in which case we extend our condolences. Understanding what all these abbreviations mean will help you out big-time in the long run. 

Pinky swear.

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