Who knows what math cross multiplication is all about

The method of cross multiplication is simply as follows: 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 addition are equal to the primary term coefficient.

Cross multiplication can factor certain quadratic trinomials. The key to this method is to decompose the quadratic term coefficient a into two factors a1, a2 of the product a1·a2, the constant term c into two factors c1, c2 of the product c1·c2, and make a1c2+a2c1 exactly the first term b, then you can directly write the result: ax 2 + bx + c = (a1x + c1) (a2x + c2), 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. Basic formula: x 2 + (p + q) + pq = ( + p ( q) The so-called cross multiplication method is to use the inverse operation of the multiplication formula (x+a)(x+b)=x 2+(a+b)x+ab to factorize.

For example: a 2 + 2 a-15 = (a + 5) (a - 3).

It's factorization, and if you get used to it, you just need to make up the numbers.

Cross multiplication is one of the 12 methods in factorization, and the other eleven are all derived from pure feasts: 1 group decomposition method 2Addition method 3

Method 4Factoring Theorem (Formula Method) 5Commutation method 6

Principal Element Law 7Special Value Method 8Pending coefficient method 9

Double Cross Multiplication 10Quadratic polynomial 11Tigong because of the hail silver method.

Cross multiplication is another basic method that needs to be prioritized when using a perfectly squared formula that cannot be factored, and is based on the identity 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 our mind is whether we can use a perfect square formula. After verification, it can be seen that this method is not possible, so consider the cross multiplication method, find two numbers such 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 has the sum equal to 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

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

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.

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.

In some quadratic trinomials, the coefficients of the first term and the third term can be decomposed into the product of two numbers respectively, and then the quadratic trinomial formula can be factored with the help of the method of drawing cross lines, which is called cross multiplication

1 1 = 1 (quadratic coefficient).

ab=ab (constant term).

1 a+1 b = a+b (primary term coefficient).

It is necessary to put a quadratic trinomial formula with a coefficient of quadratic term that is not 1.

Wheel and When factoring the equation: if the constant term q is positive, then decompose it into two homogeneous factors, whose sign is the same as that of the coefficient p

If the constant term q is negative, then decompose it into two heterogeneous factors, where the factor with the greater absolute value has the same sign as the coefficient p of the primary term

For the decomposed two factors, it is also necessary to see whether the sum of their spare modes is equal to the number p of the primary term

It's very simple, and it is more understandable such as:

x squared - 5x + 6 = 01-2

1-3 is: (x-2)(x-3)=0

That's right, the two on the left are the coefficients of x square, the two numbers on the right are the coefficients of x, and the succession is the constant behind it, and then the factorization is decomposed, but not all of them are applicable, thank you for adopting.

is the a of the binary equation

C is divided into two numbers, and then the product of the decomposed numbers of ac is subtracted by subtracting equal to b

In some quadratic trinomials, the coefficients of the first term and the third term can be decomposed into the product of two numbers respectively, and then the quadratic trinomial formula can be factored with the help of the method of drawing cross lines, which is called cross multiplication

1 1 = 1 (quadratic coefficient).

ab=ab (constant term).

1 a+1 b = a+b (primary term coefficient).

It is necessary to put a quadratic trinomial formula with a coefficient of quadratic term that is not 1.

Just factor it up: if the constant term q is positive, then decompose it into two homogeneous factors whose sign is the same as the sign of the coefficient p

If the constant term q is negative, then decompose it into two heterogeneous factors, where the factor with the greater absolute value has the same sign as the coefficient p of the primary term

For the two factors that are decomposed, it is also necessary to see whether their sum is equal to the coefficient p of the primary term

This is really difficult to explain, you ask the teacher, see the method he demonstrated, and then you can set this method, to be honest, the key is to "make up", many times you can't do cross multiplication because you can't make it up

If you can't explain it clearly, you can ask your teacher.

Below, however.

1 6+1 (-3)=-3 (this step is miscalculated, 1*6+1*(-3)=3) is obviously equal to 3 and not minus three.

x-3)(x+6)=0

1 -3

x-3)(x+6)=

Another example: 2 -5

2x-5）（6x+2）=0

The row on the left is the coefficient of the x-square, and the right is the constant term, just fill in the x on the left.

-6 3=-18 , the -18 obtained is a constant term, and the primary term is obtained with -6+3