Putting a common How is this done and what is needed for? Clear explanation and illustration for a better understanding!
Putting a common factor in brackets – is one of the main transformations in algebra, which allows you to simplify the expression by highlighting the total factor of all members in parentheses. This is a useful mathematical action that allows you to reduce the recording and more visualize the expression.
Imagine that we have an expression (4x + 8y + 12z). To pass the common factor by the brackets, we must find the largest common divider for all members (4, 8 and 12). In this case, the largest common divisor is the number 4. Having divided each member by 4, we will receive (1x + 2y + 3z). Now we can take the total factor 4 by parent and write the expression as 4 (x + 2y + 3z).
Determining the removal of the total factor by the brackets in mathematics
Simple explanation and examples
Why you need to take the common factor by the brackets
Benefits and examples of use
How to put the common factor in brackets
Steps and good examples
How to verify the correct issuance of a phone number lead common factor
Determining the removal of the total factor by the brackets in mathematics
If there are several terms or factors with a common factor inside the brackets, then it can be braced by simplifying the expression. In other words, you can divide each element inside the brackets into a common factor and write it in front of the bracket, and reduce the expression inside the brackets by this factor.
Example:
Original expression: 3x + 6y
Total multiplier: 3
We take out the total factor by the brackets: 3 (x + 2y)
Thus, by passing the common factor in brackets, we get a more compact and readable expression.
Simple explanation and examples
Original expression Expression after the common factor
In each example, we highlighted a common factor and wrote it in brackets. Note that inside the brackets we get the sum or difference of numbers that can be simplified. Thus, passing the common factor by the brackets, we simplify the for business operations expression and make it more compact.
Why you need to take the common factor by the brackets
By passing the total factor by the brackets, we reduce the number of operations and simplify the calculations. This is especially useful when working with large and complex expressions, where numbers and variables can be repeated in different brackets.
Consider an example: we have the expression 2x + 4y + 6x + 8y. We can take out a total factor of coefficient 2 and get: 2 (x + 2y) + 6x + 8y. Here we reduced the number of operations, simplified the expression and made it more understandable for further manipulations.
Thus, the removal of the common factor by the brackets is an important technique for working with algebraic expressions. It allows you to simplify and structure the expression, save time and effort in computing, and also facilitate further mathematical manipulations and analysis.
Benefits and examples of use Simplification of expressions:
Putting a common Putting a common factor in parentheses allows you to reduce complex expressions and bring them to a simpler form. This simplifies further computing and improves understanding of mathematical operations.
2. Time saving:
Putting a common factor in brackets allows you to reduce the number of operations that must be performed when solving the mathematical equation. This saves time and simplifies the process of solving problems.
3. Readability:
Simplification of expressions by removing the common factor by belize lists parentheses makes mathematical formulas and equations more readable and understandable. This allows you to more easily monitor the logic and progress of solving the problem.
