I would like to ask, how is cross multiplication calculated?

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 then the addition are equal to the primary term coefficient. In fact, it is to use the inverse operation of the multiplication formula (x+a)(x+b)=x 2+(a+b)x+ab to factorize.

Cross multiplication can factor certain quadratic trinomials. For an integer of the form ax 2+bx+c=(a1x+c1)(a2x+c2), the key to the method is to decompose the quadratic coefficient a into the product a1·a2 of the two factors a1 and a2, decompose the constant term c into the product c1·c2 of the two factors c1 and c2, and make a1c2+a2c1 exactly the coefficient b of the primary term, then the result can be directly written: ax 2+bx+c=(a1x+c1)(a2x+c2).

When using this method to decompose a factor, it is important to observe, try, and realize that it is essentially the inverse 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）χ+pq=（χ+p）（χq）。

The above is the official introduction, simply put, for the quadratic trinomial ax +bx+c, if a=a1*a2, c=c1*c2, and a1*c2+a2*c1=b

then ax +bx+c=(a1x+c1) (a2x+c2).

Hehe, you send the question in, I can help you.

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.

x^2+3x-4

Cross multiplication is to treat a coefficient of x 2 as 1x1

The constant term is treated as -1x4

x1 4 makes the cross multiplication = x term coefficient 3

x^2+3x-4=(x-1)(x+4)

6x^2-x-1

x3 16x 2-x-1=(2x-1)(3x+1)I wish you a happy and prosperous future! (If you don't understand, ask again, please adopt it in time, thank you!)

For the quadratic equation ax 2+bx+c=0 (only x is an unknown number, the other letters are known numbers, a is not 0, of course the equation is solvable in the range of real numbers), then it can be solved by cross multiplication, first decompose a into m*n, and c into p*q, but m, n, p, q (possibly negative) must meet the condition m p, m*q+n*p=b, that is, the sum of the oblique diagonal product should be b, then the square.

n q can be reduced to (mx+p)*(nx+q)=0, and the value of the unknown x can be solved.

For example, 2x 2-5x+3=0, according to the above, first 1 -1 exactly satisfies 1*(-3)+1*(-1)=-5, the equation.

In the end, it can be reduced to (x-1)*(2x-3)=0, then the value of x is 1 or 3 2

Do more special topics and find typical questions to do. I won't ask the teacher or look up the information. Listen carefully in class, and it's basically fine.

x^2+3x-4

Cross multiplication is to treat a coefficient of x 2 as 1x1

The constant term is -1x41-1

x1 4 makes the cross multiplication = x term coefficient 3

x^2+3x-4=(x-1)(x+4)

6x^2-x-12-1

x316x^2-x-1=(2x-1)(3x+1)

Cross multiplication: first decompose the quadratic coefficients, which are written in the upper left and lower left corners of the cross line; Then decompose the constant terms, which are written in the upper right corner and the lower right corner of the cross line; Then cross multiply and find the algebraic sum so that it is equal to the coefficient of the primary term.

Example--- factoring 5x +6xy-8y.

Analysis: This polynomial can be regarded as a quadratic trinomial about x, and -8y is regarded as a constant term, when decomposing the quadratic term and the coefficient of the constant term, only 5 and -8 need to be decomposed, and after decomposition with a cross line, after observation, a suitable group is selected, i.e.

Solution 5x +6xy-8y = (x+2y)(5x-4y)

It is pointed out that the original formula is decomposed into two one-time expressions with respect to x and y.

Example problem--- solution (x-y)(2x-2y-3)-2=(x-y)[2(x-y)-3]-2

2(x-y)²-3(x-y)-2

(x-y)-2][2(x-y)+1]

x-y-2)(2x-2y+1).

It is pointed out that the yuan x and y are replaced by (x+y), and (x+y) is the yuan, which is the "exchange method".

For example, x-square+2x+4=0 is solved by cross multiplication (x+2)(x+2)=0, and the right side of the equal sign must be 0