1 December 2023

Once you start in the world of mathematics, you realize that there are endless properties that, in the end, help us to better understand the resolution of a problem. From the earliest stages of learning, we are taught what the associative, commutative and distributive properties. In the same way, they explain to us what a subset in mathematics And many other things.

For whatever reason, some people have not been able to understand what the distributive property is and what it is for. In this article we will provide you with all the information related to this point and that, regardless of academic levelit helps a lot.

Concept and definition of the distributive property

Explain what is the distributive property It’s pretty easy, since it has a lot to do with multiplication. As its name indicates, it is a property that equally distributes the multiplication of two or more like terms. In the same way, it can also be defined as one of the many properties of multiplication and that it is closely related to addition and subtraction.

To understand this in better detail, let’s imagine that we have two sets that are made up of the addition or subtraction of their terms. For example, we have the set or polynomial X, which has 2 terms; we have the polynomial Y, which has a unique polynomial. Well, what the distributive property does is multiply the term of the polynomial Y by all the elements of the set X. Visually, it would look like this: 2Z (4X + 5Y).

The result of this, if we apply the distributive property, would be as follows: 8ZX + 10ZY. As you may have noticed, the distributive property allows you to distribute the term you are multiplying by everything inside the parentheses. One point to keep in mind is that the signs must always be respected and taken into account.

In the example we have given, the result was positive, since the sign of all the terms is positive. However, there may be situations where one of the elements to be multiplied is negative. In such a case, one would have to apply the distributive property, as it would normally be done, with the difference that the property of signs must be applied.

This tells us the following:

  • More for less is less. (+)*(-) = (-)

  • More for more, is more. (+)*(+) = (+)

  • Less for less is more. (-)*(-) = (+)

The reason why we are telling you this is because the distributive property also applies to the operative signs of addition and subtraction. In fact, the distributive property in a certain way also applies to signs when there is a division in between.

What is the distributive property of addition?

Taking into account everything explained, the distributive property has an addition part. That is, at the time of do the multiplication and distribution of it For all elements involved in an equation or polynomial, there must be a sum of like terms. Basically, this property tells us that after making the distribution, the equation will be adding all its terms. It is necessary to take into account that this is only applicable when each term is positive. Otherwise, it will become an algebraic sum.

What is the distributive property of subtraction?

In mathematics, subtraction is considered to be the inverse of addition. Therefore, there is not much difference in terms of what was explained in the previous paragraph. However, there are a couple of important points that we should mention and keep in mind.

  • When doing a multiplication with a negative sign between two or more terms, it is necessary to apply the sign property.

  • If two terms with a negative sign are multiplied or divided by each other, the result remains positive.

What is the distributive property of multiplication?

As such, it is a property that is closely linked to multiplication. Therefore, when it comes to a multiplication between several numbers or terms, the distributive property is applied automatically. This applies to algebra, mathematics, analytical geometry, and even physics and chemistry.

What is the distributive property in equations?

Regarding the equations, there is no difference when applying the distributive property. However, since it is something more complex than a simple polynomial, there are many other aspects that must be taken into account. For example, in a mathematical or physical equationthere are terms that are raised to a certain power, there are numbers and variables in the denominator, independent variables and much more.

The reason why we are telling you this is because, having so many more complex mathematical operations, a simple distributive will not suffice. It is necessary that all these aspects are taken into account so that, when applying said property, the equality continues to be maintained and the mathematical errors that are usually made do not occur.

Some of the examples that we can give you in this regard are when there is a term with a square root. This simple fact implies having to check if there are more square roots or with different indices. If there are, one of the following will have to be applied. radical properties in order to have everything in balance and that this equation can be solved. The same applies and can be perfectly combined with terms that are raised to X powers or are clearly exponential.

If it is the latter case, you will also have to consider the property of exponents as you apply the distributive property. As you will notice, it is not simply multiplying a single element by all the terms within an equation. It is knowing what to do and why according to each particular case, and when it comes to equations, it is more complicated.

How to explain the distributive property to children?

each one has one way of explaining math. However, this is a property that is vital to know and understand well, therefore, it is necessary and important to know how to explain this. The easiest way, or at least, the one that I would implement would be as follows:

  • Imagine that you have an apple in one hand and a bag with different fruits in the other hand.

  • By multiplying one by the other, it will allow me to have a total result of everything I have.

  • Now for distributive propertiesthe idea is to take the apple in the right hand and multiply it by each of the fruits in the bag.

  • In the end, the result will be a multiplication of apple for each of the fruits.

After having done this, it can be taken to the mathematical field. In this way, you can now apply practical examples with simple polynomials. You can have two polynomials where one of them has a single term, while the second has two. The same action explained with the fruits is carried out, but with each term.

Once this has been understood and enough examples have been done, you start to increase the difficulty a bit. In such a way that they will no longer only be two-term polynomials, but it will be from 3 onwards. Once this has been mastered to some degree, one thing you can do is change the math operation signs. That is, instead of having everything positive, you go interspersing positive and negative terms.

It takes a lot of practice to get to this point. After you have a good grasp of the basics of the distributive property, it is time to move on to its application in mathematical equations. In fact, to make it more complex, you can apply radicals, terms raised to the X power, and much more.

Examples of the distributive property in algebra and mathematics

Throughout the article we have given you some examples of how to apply this property. However, we want to give you some more specific ones so that you understand how the result of it should be.

With those three examples, you have enough at a basic level to learn how to solve mathematical problems and where you can apply the distributive property. Keep in mind that what is shown is quite basic and only equations of the first and second degree will be applied. You can take this as a reference and add a little more difficulty to it.

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