What is cross multiplication and what is cross multiplication

Cross multiplication is essentially a form of simplified equation that can factor quadratic trinomials, but it is important to pay attention to the symbols of the coefficients. The method of cross multiplication is simply as follows: the left side of the cross is multiplied equals the quadratic term, the right side multiplied is equal to the constant term, and the cross multiplication and addition are equal to the primary term.

In fact, it is to use the inverse operation of the multiplication formula (x+a)(x+b)=x + (a+b)x+ab to factorize.

Method steps.

Clarify the concept and core of cross multiplication.

<> let's take a look at this multiplication formula (x+a)(x+b), we can easily solve (x+a)(x+b)=x +(a+b)x+ab. Now look at it backwards.

How do you write the result when you break it down like this? Let's move on to the factoring of x + (a + b) x + ab.

If the quadratic coefficient is not 1, how can it be decomposed? Let's take a look at this example.

Let's take a look at the application of cross multiplication in factoring.

<> learn about the application of cross multiplication to solving equations.

Cross multiplication for factoring can simplify our calculations and is a very practical method. However, not all factoring can be done using cross multiplication, and we should accumulate experience in the process of doing problems and judge whether this method can be used as soon as possible.

Cross multiplication is a method used to solve a quadratic equation when solving a quadratic equation, which is based on whether the coefficient of the quadratic term and the constant term can be split into the product of four numbers to solve the equation, as shown in the figure below.

Cross multiplication is factorization.

One of the 12 methods, the other eleven are: 1 group decomposition method 2Addition method 3Matching method.

4.Factoring theorem (formula method.

5.Commutation method 6Principal Element Law 7Special Value Method 8Pending coefficient method.

9.Double Cross Multiplication 10Quadratic polynomial 11Mention the common factor method.

Cross multiplication is the use of a perfectly squared formula.

Another basic method that needs to be prioritized when not factoring is based on the identity that is determined by multiplication

x+a)(x+b)=x^2+(a+b)x+ab

The formula that has evolved from ——

x^2+(a+b)x+ab=(x+a)(x+b)．

In a sense, the cross multiplication method is also the use of the formula method, which is the third basic method for decomposing the quadratic trinomial formula x 2+px+q with a quadratic coefficient of 1 The idea of using this method is to find two numbers a and b, so that their product ab is equal to the constant term q, and the sum is equal to the coefficient p of the primary term Once you find such two numbers, then you can decompose the polynomial x 2+px+q into (x+a)(x+b).

For example, when factoring x 2+10x+16, since it is a quadratic trinomial, the first thing that comes to mind is whether we can use the perfect square formula? It has been verified that this method is not possible, so consider the cross multiplication method and look for two numbers so that their product is equal to 16 and the sum is equal to 10 To find such two numbers, we generally only need to consider positive integers first.

Since there are only three groups of two positive integers whose product is equal to 16, 2 and 8, and 4 and 4, the next step is to verify which group of sum equals 10 Obviously, in these three groups of numbers, only 2+8=10, so 2 and 8 are the two numbers we are looking for

Thus, x2+10x+16 can be decomposed into (x+2)(x+8).

Why is this factorization method called cross multiplication? This is because when looking for such two numbers, for the sake of convenience and intuitiveness, we generally draw the following simple cross "cross" diagram, decompose the quadratic term x 2 into x times x, decompose the constant term 16 into the multiplication of all possible two integers, and then find a group of sum equal to the coefficient of the primary term 10 Because of this "cross diagram", this factorization method is called cross multiplication

Cross multiplication is one of the factorization methods, which means that the multiplication of the left side of the cross is equal to the quadratic term coefficient, the right side multiplication is equal to the constant term, and the cross multiplication and addition are equal to the primary term coefficient. In fact, it is to use multiplication formula operations to factorize.

When solving the proportion, primary school students can use the cross multiplication method, which can find the value of the proportion by using the product of two outer terms equal to the product of two internal terms according to the basic properties of the proportion.

Also known as factorization, it is one of the steps in solving binary equations. The coefficient of the second element is divided into the product of two constants, the above and the following are shown, and the constant term is also the same, and then the upper left is multiplied with the lower right + the lower left is multiplied by the upper right = the coefficient of the first element.

Cross multiplication is an arithmetic method used to multiply two multi-digit numbers.

It is also known as vertical multiplication, column vertical multiplication, etc. The principle of this method is to pair and multiply each of the two numbers by pairing each other, and then add the result. Write the two numbers together vertically, and everyone aligns.

From right to left, multiply each of the familiar digits of one of the numbers by the number of digits corresponding to the other number to get a set of small products. Arrange the small plots in order from right to left in the corresponding position below the vertical type. Add up all the small products to get the final result.

Cross multiplication is able to efficiently calculate multi-digit multiplication and make the calculation process more standardized and easy to understand. As a result, it is widely used in both education and practical life.

Cross multiplication mantra slips smoothly:

Cross multiplication, the formula is learned, first fill in the upper left and lower right, then the upper right and lower left, multiply the isotopes, and then add the carrying, so that you can calculate the specific number of the product of the value of the trembling field. The product of the ten digits is placed in the upper left corner, and the product of the single digits is placed in the lower right corner, and the results are added to the tag in the middle. The same method can also be done in the upper right corner, lower left corner, and the result will be calculated.

After learning the formula, the cross multiplication should be used, the arithmetic problems were solved, the primary school students were all right, the mathematics was learned, and life was more exciting. <>

Cross multiplication is one of the factorization methods, which means that the multiplication of the left side of the word is equal to the quadratic term coefficient, the right side multiplication is equal to the constant term, and the cross multiplication and then addition are equal to the primary term coefficient. In fact, it is to use multiplication formula operations to factorize.

Introduction to Cross MultiplicationThe left side of the cross is multiplied equally, the right side is multiplied equals the constant term, and the cross multiplication is added to the primary term coefficient. In fact, it is to use multiplication formula operations to factorize. The cross factorization method can be used to factor (not necessarily in the range of integers) of quadratic trinomials (unary quadratics).

The procedure to decompose the common factor using cross multiplication1) Decompose the coefficient of the quadratic term and the constant term into factors respectively;

2) Try the cross chart, so that the sum of the numbers obtained after multiplying the cross lines is the coefficient of the primary term;

3) Determine the appropriate cross diagram and write out the results of factorization;

4) Inspection. Features of the cross proportionality method1.The coefficient of the secondary term is 1;

2.The constant term is the product of two numbers;

3.The coefficient of the primary term is the sum of the two factors of the constant term.

Considerations for cross multiplication

1.It is used to solve the problem of proportions between the two.

2.The resulting proportional relationship is the proportional relationship of the cardinality.

3.The total mean is placed on the diagonal bicycle, and the large number is decreased, and the result is placed on the diagonal.

Cross multiplication is one of the fourteen methods in factorization. Let's make a wide boy

Cross multiplication

The method of cross multiplication is simply as follows: the product of the left side of the cross is a quadratic term, the product of the right side of the multiplication is a constant term, and the cross multiplication and addition are equal to the primary term. The principle is to use the inverse operation of binomial multiplication to factor it.

Cross multiplication can be used to factorize quadratic trinomials (quadratic quadratic formulas). Coincidentally, for an integer like ax +bx+c=(a x+c) (a x+c), the key to this method is to decompose the quadratic coefficient a into the product of two factors a and a, and the constant term c into the product of two factors c and c, and make a c +a c exactly equal to the coefficient b of the primary term. Then you can write it directly as a result:

ax²+bx+c=(a₁x+c₁)(a₂x+c₂)。

When using this method to decompose factors, it is important to observe, try, and realize that it is essentially the inverse process of binomial multiplication.

When the first coefficient is 1, it can be expressed as x + (p + q) x + pq = (x + p) (x + q); When the first coefficient is not 1, it often takes several tests, and it is important to pay attention to the symbols of each coefficient.

Factorization

The deformation of a polynomial into the product of several integers is called factorization of the polynomial, also known as factorization of the polynomial.

The form of converting a polynomial into the product of several integers in a range is called factorization of the polynomial, also known as factorization of the polynomial.

Factorization is one of the most important identity deformations in middle school mathematics, which is widely used in elementary mathematics, and is also widely used in mathematical root plotting and solving one-dimensional quadratic equations, and is a powerful tool for solving many mathematical problems.

The factorization method is flexible and skillful. Learning these methods and techniques is not only necessary for mastering the content of factoring, but also has a very unique role in cultivating problem-solving skills and developing thinking skills. Learning it can not only review the four operations of integers, but also lay a good foundation for learning fractions; Learning it well can not only cultivate students' observation, thinking development, and calculation skills, but also improve their ability to comprehensively analyze and solve problems.

Hello, the method of cross decomposition method is simply a dry situation: the left side of the cross is multiplied equal to the quadratic term, the right side of the filial piety is not carefully multiplied equal to the constant term, and the cross multiplication and then added is equal to the coefficient of the primary term. In fact, it is to use multiplication formula operations to factorize.

Example.

The cross multiplication method is a kind of solution square rolling hole method used in the old cracking of the unary quadratic equation, which is based on whether the quadratic coefficient and the constant term can be split into the product of four numbers to solve the equation, as shown in the following figure.

The "multiplication method of ten digging" is used to solve one-dimensional quadratic equations, which is one of the methods of factorization, and mastering it can increase the calculation speed exponentially!

First, the rationale.

Second, how to use.

Using the inverse of the above equation, the left equation is made up only to the right of the known equal sign.

That is, the multiplication of the left side of the cross is equal to the coefficient of the quadratic term, the multiplication of the right side is equal to the constant term, and the multiplication of the cross and the addition of the coefficient of the primary term.

3. Scope of use.

First of all, the unary quadratic equation must be reduced to the standard form of the old celery kernel, and the right side of the equal sign must be 0.

Moreover, not all unary quadratic equations can be multiplied by cross, and cross-multiplication can only be used in an integer range if the discriminant of the root is a perfect square number.

The purpose of using the cross-multiplication method is to do a quick calculation, and if we have to use the discriminant of the root to verify whether the cross-multiplication is possible every time, it is a waste of time and defeats our original intention. So in the end, we can only do more practice and make quick judgments based on experience. If you think you can, try it quickly, and if it doesn't work, then try it again.