Correctly converting terms in math

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You will often encounter term conversions in school mathematics. But they lose their horror if you master the laws of math terms.

When changing terms, brackets must be broken.
When changing terms, brackets must be broken.

What you need:

  • actually only basic knowledge of algebra
  • and of course time and leisure for this article

Terms in math - you need to know that

  • In mathematics, a term is understood as a kind of "letter calculation", i.e. a mathematical expression that includes both Counting as well as letters (as general substitutes for numbers).
  • The expression 3 + b is just as much a term as a² + b² (part of Pythagoras) or (a + b) ² (the first binomial formula).

Term transformations - these rules must be observed

Often it is in the mathematics It is necessary to transform existing terms, often to make them simpler or to remove brackets, for example to get an overview.

In principle, simple rules apply to term transformations:

  1. You can add and subtract in terms, but only the same letters or Combinations of letters.
    2. Release the bracket - this is how it is done with terms

    Breaking the brackets with terms - as a student, you can slip into a skid. …

  2. If mixed types of calculation occur, the following applies: Point calculation (i.e. times or divided) before line calculation (i.e. plus and minus).
  3. You solve a bracket before or after a factor (no matter if number or letter) occurs by multiplying each part of the bracket with this factor.
  4. You can resolve double (or even triple) parentheses by multiplying each part of the first parenthesis by each part of the second parenthesis.

Term rewriting - these examples show the rules

The mentioned term transformations are to be explained and illustrated using corresponding calculated examples:

  1. The term 2a - 3b + ab - 7a -ab can be summarized to -5a - 3b (because 2a - 7a = 5a and ab -ab are omitted).
  2. a²: a + a x b x 3 can also be reshaped. However, you first have to calculate a²: a = a, then a x b x 3 = 3ab and you finally get a + 3ab as the term rewrite
  3. Open the bracket 3 x (a - 5b) as follows: 3 x a - 3 x 5 b = 3a - 15b
  4. Open the two brackets (x + 1) (x-2) as follows: x² - 2x + 1x - 2. You can summarize this term and get: x² - x - 2 (instead of -1x you write -x).

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