Basic Mathematical Facts: Combining Like Terms

In math, you have four main operations: addition, subtraction, multiplication, and division. Since subtraction is the reverse of addition, multiplication is repeated addition, and division is the reverse of multiplication, you will see that the other three operations are indirectly derived from addition. In this sense, there is really a binary operation in mathematics: addition. The binary operation refers to the use of a mathematical operator, such as addition, on two numbers or variables, as in x + y. Since we see how important addition is now, we must fully understand one of the most important tasks in all mathematics: combining like terms.

Similar terms they are expressions that involve the same combination of variables and their respective exponents but different numerical coefficients. The coefficients, if you remember, are the numbers in front of the variable. To put it simply, like terms are like apples and apples, oranges and oranges. Examples of like terms are 4x and 2x, gold 3 years and 9 years. To remove the abstraction from the whole thing, the student should keep in mind that as long as the expressions are similar regardless of coefficients, the terms can be added or subtracted. Therefore, 3xy and 4xy are similar terms and can be combined to give 7xy. Take away the coefficients 3 and 4, and what is left? xy.

Many times a student will not be able to arrive at the final answer to an algebra problem because at some point the like terms were not combined correctly. In more complicated math problems, expressions can get a bit more complicated. However, if you keep in mind that like terms are similar “animals,” so to speak, then, like animals, they can mate safely. If the terms are not similar, you can never combine them. The results are always disastrous. What generally helps students is to steer them away from abstraction and bring them face to face with the hard facts: if two algebraic expressions, after removing the numbers in front, look the same, then they are like terms and can be added and added. subtracted. Notice that we are only talking about the two operations of addition and subtraction, since these are the two operations that require the terms to be like before combining. Multiplication and division do not have this requirement.

Let’s look at some examples to make this perfectly clear and see where some potential problems can arise. Let’s do the examples below.

1) 3 times + 18 times

2) 8xyw – 3xyw + xyw

3) 3x ^ 2 – x ^ 2 + 6x

The first example can be thought of as 3 x and 18 x. Think of the actual letter in plastic form in child’s play. Obviously, you have 21 x or 21 x for your answer.

The second example gives an indication of when students may start to have problems. The moment more than one letter or variable is entered, students quickly become intimidated. Do not be. If you remove the coefficients on each of the terms, you will see that they are all xyw terms. The last term has a coefficient of 1, which is understood. Combining, we have 6xyw.

The third example presents an expression with exponents. Remember that the exponent, or power, only tells us how many times to use the number as a factor when multiplying by itself. So x ^ 2 tells us to multiply x by itself, that is, x ^ 2 = x * x. If you remove the coefficients in this example, you will see that you have 2 x ^ 2 terms and one x term. So you can only combine the x ^ 2 terms. The answer becomes 2x ^ 2 + 6x. Note that terms that cannot be combined simply remain as is.

The information here should make you an expert at combining like terms, as this is actually a very easy task, but an extremely important one. If you follow the guidelines set out here, you should have no more difficulty simplifying basic algebraic expressions.