Removing a common factor It possible to significantly simplify mathematical expressions and make them more compact. This is especially useful in solving equations and systems of equations, as well as in algebra and arithmetic.
Definition and essence
The essence of removing the total factor by brackets is as follows. If in the expression inside the brackets there is a common factor for all the components, then it can be bracketed, and the rest of the expression can be written in brackets. This allows you to reduce the number of multiplication operations and simplify calculations.
The removal of the common factor by
The brackets is used when working with polynomials and algebraic expressions. It can be especially useful in simplifying complex expressions and finding a common species.
To carry out the removal of the common factor, certain buy telemarketing data rules follow the brackets. First of all, it is necessary to find a common factor for all folded inside the brackets. Then divide each folded into this common factor and write the private in brackets. The rest of the expression without a common factor can be written in parentheses. The result is a simplified expression that can be further simplified or calculated.
Example Removing the total factor by parentheses
(2x + 4y) + (2x — 6y) 2 (x + 2y) + 2 (x — 3y)
3a ^ 2b — 6ab ^ 2 + 9ab 3ab (a — 2b + 3)
Common factor removal examples
Example All multiplier removal
3x + 6y 3 (x + 2y)
4a — 8ab 4a (1 — 2b)
2m ^ 2 + 10mn 2m (m + 5n)
In the first example, the expression 3x + 6y contains a total factor of 3. By removing the factor 3 from the brackets we get the expression 3 (x + 2y).
In the second example, the expression 4a —
8ab has a total factor of 4a. We take it out of brackets and get 4a (1 — 2b).
In the last example, the expression 2m ^ 2 + 10mn contains a in the new millennium getting total factor of 2m. We take it out of brackets and get 2m (m + 5n).
The removal of a common factor allows you to simplify expressions, facilitates their further calculations and is an important tool in algebra.
General multiplier removal rules
Here are the basic rules for removing a common factor:
1. We take out the total factor with the highest degree
If variables with the same bases and degrees are present in the terms or Removing a common factor subtracted, then the total factor will be the product belize lists of these variables. In this case, the total multiplier will have the highest degree with which the variable occurs.
