Mathematical cross multiplication examples, what is cross multiplication?

Example: Find the real root of the equation 3x 2+2x-1=0. Solution:

1 1 3 -1 classmates, you see, the cross-multiplication is 1 -1 and 3 1;Then add the two of them up to =2, as long as it is equal to the coefficient of the primary term in the equation, which means that this is correct. The equation is then converted to (x+1)(3x-1)=0;Solution: x=-1 or x=1 3

The brief introduction is as follows:The 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 method compares the size of the two fractions, and the real group shot is qualitatively a common score. However, it saves students the process and time to score fractions, so that it is simpler and more straightforward in one step, as long as students who can multiply, it is basically effortless when comparing the size between fractions.

Introduction:

For the shape of the enlightenment, such as ax + bx + c of the multi-collapse side envy term.

In determining whether it can be factored using the cross decomposition method.

, you can use δ=b -4ac to make a decision. When the δ is a perfectly squared number, the polynomial can be cross-multiplied in an integer range.

Cross multiplication: one of the two methods of factoring the decimation of the decade, the main content is that 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. The principle is to use the inverse operation of the multiplication formula to factorize.

The cross decomposition method can be used to factor the quadratic trinomial. The key to this method is to decompose the coefficient of the quadratic term into the product of two factors, and decompose the constant term into the product of two factors, so that the multiplication of the two terms is exactly equal to the coefficient of the primary term. When using this method to decompose factors, it is important to note 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.

Cross Multiplication Usage: Use cross multiplication to break down the common factor. The steps are as follows:

1. Take a look at this unary quadratic equation, which can be divided into three items (remember not to forget the factor), the A term is A2, the B term is 1A, and the C term is -6.

2. Item A can be decomposed into a*a, and item C can be divided into -3*2 and -2*3 or -6*1 and -1*6.

3. According to the cross multiplication method, cross multiplication gives 4 kinds of results, which are -a, a, -5a, and 5a.

4. Comparing the results with the b term, only the number contains two kinds of results that are equal to the b term, so the factor (a+3)*(a-2)=0 is obtained, and the answer a=-3 or a=2 is finally obtained.

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 is equal to the constant term, and the intersection and multiplication and addition are equal to the primary term. In fact, it is to use multiplication formula operations to factorize.

The form of dividing a polynomial into the product of several integers in a range is called factoring of the polynomial, also known as factoring 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. Using cross multiplication to solve problems is relatively fast, can save time, and the use of arithmetic is not large, and it is not easy to make mistakes.

Precautions for cross multiplication:

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

2. The proportional relationship obtained is the proportional relationship of the base.

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

This can only be matched with the method, and the cross phase multiplication is not easy to match.

4y²-8y+15=0

2y-2)²+11=0

Empty shirt state 2y-2) 0

2y-2）²+11≥11

On the left is Evergrande at 11

It is impossible to wait for the collapser to be at 0.

There is no real solution to this.

There is no solution to this equation within the range of real numbers.

3 points -4 points.

1 Slippery Quarrel Letter Servant Answer Branch 2

3x²-4x-4

Tunson guessed that the observation could be answered with -6+2=-4

So 3x move-4x-4=(x-2)(3x+2).

The quadratic term coefficient 3 is split into 1 and 3

The constant term 4 is split into -2 and 2

x-2)(3x+2)=0

Cross multiplication, factorization, and more practice, you will become proficient.

Answer: Be cautious with the case, see Tupi filial piety to take the burning film.

Under the coefficient decomposition of the quadratic term, under the decomposition of the constant term, the cross-multiplication is equal to the coefficient of the primary term.

For example, 2x +3x +1=0

1 1 crosses into addition 2*1+1*1=3 then (2*x+1)(1*x+1)=0