In math, you have four main operations: addition, subtraction, multiplication, and division. Since subtraction is the inverse of addition, multiplication is repeated addition, and division is the inverse of multiplication, you’ll see that the other three operations follow indirectly from addition. In this sense, there really is a binary operation in mathematics: addition. Binary operation refers to the use of a mathematical operator, such as addition, on two numbers or variables, as in x + y. Now that we see how important addition is now, we need to fully understand one of the most important tasks in all of mathematics: that of combining like terms.
similar terms are expressions involving 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 this in layman’s terms, similar terms are like apples and apples, oranges and oranges. Examples of like terms are 4x Y 2xPrayed 3 years Y 9 years. To remove the abstraction from this whole issue, the student should keep in mind that as long as the expressions are similar regardless of the coefficients, the terms can be added or subtracted. Therefore, 3xy and 4xy are like 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, the expressions can get a bit more complicated. However, if you keep in mind that like terms are like “animals”, so to speak, then like animals they can safely mate. If the terms are not similar, he will never be able to combine them. The results are always disastrous. What usually helps students is to get them out of the abstraction and face them with the concrete facts: if two algebraic expressions, after removing the opposite numbers, look the same, then they are like terms and can be added and subtracted. Note that we are only talking about the two addition and subtraction operations, since these are the two operations that require terms to be like before they are combined. 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) 3x + 18x
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 a child’s game. Obviously, you have 21 x or 21x as the answer.
The second example gives an indication of when students might start having problems. The moment more than one letter or variable is introduced, students quickly become intimidated. don’t be If you remove the coefficients of each of the terms, you 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 introduces an expression with exponents. Remember that the exponent, or power, only tells us how many times to factor the number 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 they are.
The information here should make you a master of combining like terms as this is actually a very easy task, but extremely important. If you follow the precepts laid out here, you should have no more difficulty simplifying basic algebraic expressions.