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Simplifying Expressions and Combining Like Terms - Concept
Expressions are put into their simplest form so as not to be confusing or too complex. One way of simplifying expressions is to combine like terms. By combining terms we can shorten and simplify our expressions, making them easier to read. Like terms often contain the same variable or variables.
As you move into your study of Algebra, there's a whole lot of vocabulary to keep straight in your brain. Here is a bunch of words we're going to go over, like terms are pieces of an expression that contain same variables raised to the same powers or same exponents. Let me give you an example, lets say I had 3x and 3x squared. Those are not like terms is because I have the same letter, I both have x's but this one has an x squared, has different exponent. If I stick in there 4x squared, now these ones would be like terms because they both have x squared pieces. Don't be thrown off by this big number out front doesn't matter if they're the same or different. To look for like terms you're only looking for the variables with the same exponents.
Those big numbers out front actually have a name and they are called "Coefficients." A coefficient is the number that is multiplied by a variable. So in these problems the coefficient was 3, that coefficient was 3, that coefficient is 4. An expression is an Algebraic statement without an equal sign, so if I were to write 3x squared plus 2 that's an Algebraic statement no equal sign, it's an expression. As soon as I stick in there an equal sign like equals 10 suddenly that became, that become, that becomes an Algebraic equation. Equation means it has that equal sign, and one more other thing to keep in mind, sometimes in your text book if your text book has like kind of tricky wording it'll say something like, simplify or will say simplify 3x squared plus 2x squared and that would mean you will combine like terms. Or it might write 3x squared plus 2x squared equals, with nothing there. Don't be confused, this is not an equation suddenly; this doesnt, isn't actually a proper Math notation because we need to have 3x squared plus 2x sqyared equal to 5x squared, now it becomes an equation. So things to keep in mind are these vocabulary words, one more time with like terms you're looking at the exponents and their powers only you don't care about the coefficients those can be different.
An expression is just a Mathematical statement without an equal sign, as soon as I stick an equals to something else that's when it becomes an equation.