Simplifying Algebraic Expressions (1-8)

Simplifying Algebraic Expressions

Vocabulary:   Term - a number, a variable, or product of numbers and variables. Note: Terms are
                                  separated by addition, or subtraction signs.
                      Coefficient - an number that is multiplied by a variable.
                      Variable - a letter, or symbol used to represent a changeable quantity.
                      Like Terms - having the same variable, variable with the same exponent (power)
                                           or no variable.
Example:       3n + n + 5...Look at the variable. How many n's are represented?
                      3n + n = 4n.                  Therefore, the expression is 4n + 5

STEPS TO FOLLOW:

First:

Define "like terms" by their variables and powers. In algebra, "like terms" have the same configuration of variables, raised to the same powers. In other words, for two terms to be "like", they must have the same variable or variables, or none at all, and each variable must be raised to the same power, or no power at all. The order of variables within the term does not matter.For example, 3x² and 4x² are like terms because each contains the variable x raised to the second power. However, x and x² are not like terms because each term has x raised to a different power. Similarly, -3yx and 5xz are not like terms because each term has a different set of variables.

• Second:
  Factor by writing numbers as the product of two factors. Factoring is the concept of representing a given number as the product of two factors multiplied together. Numbers can have more than one set of factors - for instance, the number 12 can be formed by 1 × 12, 2 × 6, and 3 × 4, so we can say that 1, 2, 3, 4, 6, and 12 are all factors of 12. Another way of thinking of this is that a number's factors are the numbers by which it is evenly divisible.
  

  • For example, if we wanted to factor 20, we might write it as 4 × 5.
  • Note that variable terms can also be factored - 20x, for instance, can be written as 4(5x).

  Prime numbers can't be factored because they are only evenly divisible by themselves and 1.
  Third:
  

  Use the acronym PEMDAS to remember the order of operations. Sometimes, simplifying an expression means nothing more than performing the operations in the expression until no more can be done. In these cases, it's important to remember the order of operations so that no arithmetic errors are made. The acronym PEMDAS can help you remember the order of operations - the letters correspond to the types of operations you should perform, in order. If there is multiplication and division in the same problem, you must complete those operations from left to right when you get to that point. The same goes for addition and subtraction. The image above gives the incorrect answer. The last step did not work the addition and subtraction from left to right. It did the addition first. It should show 25-20 = 5 and then 5 + 6 = 11.
  

  • Parentheses
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction 

  
  VIDEO HELP
   https://learnzillion.com/lessons/3275-simplify-algebraic-expressions-by-combining-like-terms
  
  https://www.youtube.com/watch?v=0SYsdGEUjoI
  
  https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-manipulating-expressions/v/combining-like-terms