How to match mathematical cross multiplication, mathematical cross multiplication

Cross multiplication is more difficult to learn, but once we learn it, using it to solve problems will bring us a lot of convenience, and here are some of my personal insights on cross multiplication.

1. The method of cross multiplication: the left side of the cross is equal to the quadratic term coefficient, the right side is equal to the constant term, and the cross multiplication and then the addition is equal to the primary term coefficient.

2. The usefulness of cross multiplication: (1) Use cross multiplication to decompose factors. (2) Use cross multiplication to solve a quadratic equation.

3. Advantages of cross multiplication: the speed of solving problems by cross multiplication is relatively fast, which can save time, and the amount of calculation is not large, and it is not easy to make mistakes.

4. Defects of cross multiplication: 1. Some problems are relatively simple to solve by cross multiplication, but not every problem is simple to solve by cross multiplication. 2. Cross multiplication is only applicable to quadratic trinomial type problems. 3. Cross multiplication is more difficult to learn.

5. Cross multiplication problem solving example:

1) Use cross multiplication to solve some simple and common problems.

Example 1: Factor m +4m-12.

Analysis: The constant term -12 in this question can be divided into -1 12, -2 6, -3 4, -4 3, -6 2, -12 1, and -12 when -12 is divided into -2 6.

Solution: Because 1 -2

So m +4m-12 = (m-2) (m + 6).

Example 2: Factor 5x +6x-8.

Analysis: 5 in this question can be divided into 1 5, -8 can be divided into -1 8, -2 4, -4 2, -8 1. This problem is met when the coefficient of the quadratic term is divided into 1 5 and the constant term is divided into -4 2.

Solution: Because 1 -2

So 5x +6x-8 = (x+2) (5x-4).

There is a skill on the soso to look up the mathematical cross multiplication.

Summary. Cross multiplication is one of the fourteen methods used in factorization, and the other thirteen are: 1

Mention the common factor method 2Formula Method 3Double Cross Multiplication 4

Rotational symmetry 5Addition 6Matching method 7

Factoring theorem 8Commutation method 9Comprehensive division 10

Principal Element Law 11Special Value Method 12Pending coefficient method 13

Quadratic polynomials.

Cross multiplication is one of the fourteen methods in the decomposition of this tung bend of the Sen stuffy factor, and the other thirteen kinds of round annihilation are: 1Mention the common factor method 2

Formula Method 3Double Cross Multiplication 4Rotational symmetry 5

Addition 6Matching method 7Factoring theorem 8

Commutation method 9Comprehensive division 10Principal Element Law 11

Special Value Method 12Pending coefficient method 13Quadratic polynomials.

Can you add, I don't quite understand it.

The method of cross multiplication is simply as follows: the multiplication of the left side of the cross is equal to the coefficient of the quadratic term, the multiplication of the right side of the imitation plexus 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 multiplication and sakura formula operation to perform factorization.

You can use the multiplication method of the cross with a stool to turn it into 10 2 0, and divide the stupid wisdom to solve the factor to get (2 1) (5 2) 0, because Bi is 1 2, 2 5

Cross multiplication can factor certain quadratic trinomials. The key to this method is to decompose the quadratic term coefficient a into two factors a1, the product of a2 a1 6 1a2, and the constant term c into the product of two factors c1 and c2 c1 6 1c2, and make a1c2+a2c1 exactly a term b, then the result can be written directly: when using this method to decompose the factor, we should pay attention to observe, try, and realize that it is essentially the inverse process of binomial multiplication.

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.

Example 1: Factor 2x 2-7x+3.

Analysis: First decompose the coefficient of the quadratic term, which is written in the upper left corner and the lower left corner of the cross line, and then decompose the constant term and divide.

Don't write in the upper right and lower right corners of the crosshairs, then cross and multiply to find the algebraic sum so that it is equal to the coefficient of the primary term.

Decompose quadratic coefficients (take only positive factors):

Decomposition Constant Term:

The method of drawing crosses is used to represent the following four situations:

7 After observation, the fourth case is correct, and this is because after cross-multiplication, the sum of the two algebras is exactly equal to the coefficient of the first term 7

Solution 2x 2-7x+3=(x-3)(2x-1)

In general, for the quadratic trinomial formula ax2+bx+c(a≠0), if the quadratic term coefficient a can be decomposed into the product of two factors, i.e., a=a1a2, and the constant term c can be decomposed into the product of two factors, i.e., c=c1c2, a1, a2, c1, c2, arrange as follows:

a1 c1 ╳a2 c2

a1c2+a2c1

Multiply according to the diagonal crossing, and then add to get a1c2+a2c1, if it is exactly equal to the primary term coefficient b of the quadratic trinomial ax2+bx+c, that is, a1c2+a2c1=b, then the quadratic trinomial can be decomposed into the product of two factors a1x+c1 and a2x+c2, i.e.

ax2+bx+c=(a1x+c1)(a2x+c2).

This method of factoring a quadratic trinomial equation by drawing a cross line to decompose the coefficient is often called cross multiplication.

The coefficient of the primary term in cross multiplication is the sum of the two numbers. The constant term is the product of two numbers! The premise is that the quadratic coefficient is one.

Divide the A and C terms in the equation into two factors. Multiply the first factor of term A by the second factor of term C, and then multiply the other two numbers together to get two products. Add or subtract these two numbers to give you a coefficient of item b.

If you do more, you need to be proficient.

It is made up, and the coefficient and constant term of equation 2 are divided into two numbers and multiplied respectively, for example: solve equation:

2x squared - 3x + 1 = 0 can be split like this.

In four groups: 2x1

2x-1x1

x-1x1x-12x1

2x-1 then add the two numbers multiplied diagonally, and if the coefficient is the same as the first term, it can be understood:

2x-1)(x-1)=0

x = 1 2 or 1

The basic idea is to decompose the binomial coefficient l of the binomial lx +mx+n into a*b, and decompose the constant term n into c*d, when the condition is satisfied: ad+bc=m, the factorization is completed.

The basic principles of cross multiplication are relatively easy to understand with the help of graphics:

When solving the problem, you only need to decompose the binomial coefficient into a*b, write ab on scratch paper, as described in the figure above, in the same way, decompose the constant term into c*d, cd is written in the corresponding position, calculate ad+bc, and see if it is equal to the coefficient of the primary term.

Here are a few things to note:

In many cases, the coefficient of the quadratic term is 1, that is, l = 1, so a = 1, b = 1, and the two 1s can be written directly in the corresponding position.

Lmnabcd has positive and negative signs, so it is necessary to pay attention to the positive and negative signs when decomposing [generally speaking, the coefficient of the quadratic term l of the factor is positive, if l is negative, the negative sign is directly extracted before the whole formula, and after the mn is changed to the corresponding sign, it becomes the case that l is positive and then calculated].

Regardless of whether ln is prime or composite, don't forget about the factorization of 1*l and 1*n.

Here are a few tips about positive and negative signs (only discuss the case where l is positive, ab is positive; If l is negative, change the sign first).

If n is negative, then c d is positive and negative, take c positive d negative, when m is positive, then bc>ad [when l = 1, then c >d, that is, the large factor is positive], when m is negative, the small one is positive;

If n is positive, when m is positive, cd is positive; When M is negative, CD is negative.

Factorization requires more observation and more connections, and it is important to be proficient in the four-rule operation of one or two digits and the factorization of composite numbers, so as to be able to respond quickly. The mistakes are made in the case of plus or minus signs and 1*n, and you can become proficient with more practice.

Decompose the coefficient of the quadratic term and the constant term (with the preceding sign) into the form of two products, write them as vertical columns, multiply the two verticals by crossing and multiply the sum of the second term, and finally add them horizontally and write them into the form of the product.

First, the quadratic term is decomposed into two factors, and then the product of the multiplication of the two numbers is a constant term, and the sum of the two numbers is the coefficient of the primary term. Then multiply the sum of the above factors plus the number of faces by the sum of the following factors plus the following numbers, for example: 2x square + 3x-2 = 0

Can be decomposed into (2x-1)(x+2)=0. So x1 = 1 2

x2=-2

From point to surface. For example, x-3x+2:2 is split into (1)*(2), (1+(2)=3[x-1][x-2], such as x*x-3x+4:

4 is split into (4)*1, (4)+1=3.[x-4][x+1]

To sum it up in one paragraph. Thank you.