What does crossover cross multiplication mean in factorization?

The decomposition of the same formula is multiplied by the cross of another synchronous decomposition, for example, a squared + 5ab + 4b squared = 0, a square can be decomposed into two a multiplication, 4b square can be decomposed into 4b multiplied by b, cross multiplication to obtain ab + 4ab = 5ab is equal to the intermediate term 5ab, so the above equation is factored into (a + 4 ab) (a + b).

This is the easiest and fastest way for you to solve equations in middle and high school, but it needs to meet certain conditions

x*x+6x+9=0

The coefficient of x is 1, and it is divided into 1 and 1 (it can also be regarded as none) The constant is 9, and your purpose is to split 9 into 2 numbers, and these two numbers are multiplied to get a constant, and the coefficient of the term is 6, so if you split 9 into 3 and 3, x solves it as 2 of the same solution, and the solution of this equation is 3

This is available when the right side is equal to 0 and the coefficient of the 2nd term is 1.

Cross multiplication, cross multiplication isFactorizationOne of the fourteen methodsThe method of cross decomposition method is simply as follows: the left side of the cross is multiplied equals the quadratic term, the right side is multiplied equals the constant term, and the cross multiplication and then added is equal to the second term of the first place. In fact, it is to use multiplication formula operations to factorize.

The cross decomposition method can be used to decompose the factors of quadratic trinomials (unary quadratic formulas).

It doesn't have to be in the integer range).

Decide. For polynomials of the form ax + bx + c.

To determine whether it can be factored using the cross decomposition method, it can be determined using δ=b -4ac. When δ is a perfectly squared number.

, you can cross-multiply the polynomial in an integer range.

Difficulty: Flexible use of the cross decomposition method to decompose factors. Because not all quadratic polynomials can be factored by cross multiplication. Sakura years old.

Focus: Correctly use the cross decomposition method to factor some quadratic trinomials whose coefficient is not 1.

Precautions. The first point is to solve the problem of proportionality between the two.

The second point: the proportional relationship obtained is the proportional relationship of the base.

The third point: the total mean is put **, and the diagonal is implied.

, the large number decreases, and the result is placed on the diagonal.

Cross-multiplication factorization is factorization through the multiplication formula.

1. Factorization: When we learn one-dimensional quadratic equations, one of the most commonly used methods is actually factorization. Because the calculation process of factorization is relatively simple, we only need to calculate the result according to the formula.

There are many ways to factorize, and crisscrossing is one of them.

2. Cross method: Cross multiplication is the easiest way to solve a quadratic equation. Because we only need to decompose the formula into a multiplication formula to find the result directly.

After we decompose it, a new formula will be formed, and our calculation result is actually hidden in the formula.

3. Unary quadratic equations: When we learn unary quadratic equations, we will learn how to decompose unary quadratic equations. For the decomposition of a quadratic equation, we will use crosses, but the use of crosses is case-specific.

If we decompose it, the amount of calculation is relatively large, and the results may not be able to produce the results of the town, Yu Lu Bo can try the formula method.

So, cross-factoring is a lot of things that can be easy to calculate, but not in all cases.

Criss-cross methodFactorization is an important method for determining the composition of binary mixtures. Cross multiplicationThe method is that the left side of the cross is multiplied equally equals the quadratic term coefficient, the right side is multiplied equals the constant term, and the cross multiplication is added to the primary term coefficient.

In a binary mixture system, the characteristic values of each component are additive, such as mass, volume, oxygen consumption, and molar mass.

Number of particles. At this time, the content of each component of the mixture can be calculated by the cross-cross rolling fork method.

Mathematical derivation of the criss-cross method:Let's take a look at the following two typical examples: [Example 1] The average molecular weight of the gas mixture is 30, and the volume ratio of the two hydrocarbons in the mixture is found.

Solution: Let the quantities of the two gaseous hydrocarbon substances.

They are n 1 and n 2, and the mass of the gas mixture is the sum of the masses of the two gases.

Think of x-y as a whole, so the formula is perfectly squared:

2+3(x-y)]²

2+3x-3y)²