Although cross multiplication is difficult to learn, it will bring us a lot of convenience once we learn it and use it to solve problems. The following is my personal opinion on cross multiplication. 1, the method of cross multiplication: the left multiplication of the cross is equal to the quadratic term coefficient, the right multiplication is equal to the constant term, and the cross multiplication is equal to the linear term coefficient. 2. Use of cross multiplication: (1) Cross multiplication is used to decompose factors. (2) Solving the quadratic equation with one variable by cross multiplication. Advantages of cross multiplication: it is faster to solve problems with cross multiplication, which can save time and 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 simply solved by cross multiplication. 2. Cross multiplication is only applicable to quadratic trinomial type problems. 3. Cross multiplication is more difficult to learn. 5. Examples of cross multiplication: 1). Solve some simple and common problems with cross multiplication. 1. Factorization m+4m- 12: The constant term-12 in this question can be divided into-1× 12, -2×6. -12× 1 When-12 is divided by -2×6, it conforms to the solution of this question: because 1 -2 1╳ 6, m+4m-12 = Solution: Because 2 -5 3╳ 5, the original equation can be changed to (2x-5)(3x+5)=0, so x1= 5/2x2 =-5/3 2). Solving some difficult problems by cross multiplication Example 5 Factorization 14x-67xy+ 18y: If 14x-67xy+ 18y is regarded as a quadratic trinomial about X, then 14 can be decomposed into/kloc-. 18y can be divided into y. 18y, 2y.9y, 3y.6y solution: because of 2 -9y 7╳ -2y,14x-67xy+18y = (2x-9y). Turn this polynomial into a quadratic trinomial solution 1, 1 0x-27xy-28y-x+25y-3 =10x-(27y+1) x-(28y-25y+3) 4y-37y-/kloc-0. 0x-(27y+1) x-(4y-3) (7y-1) is decomposed into [2x-(7y- 1)] solution 2, 10x-27xy-28y-x+25y-3 = (2x-7y) (5x+4y)-(x-25y)-32-7y = [(2x-7y)+65438+1cross multiplication is used for Example 7: Solving the equation about X: X-3ax+2A–AB-B = 0 Analysis: 2A–AB-B can be decomposed by cross multiplication factor: X-3ax+2A–AB-B = 0x-3ax+(2A–AB-B) = 0x-3ax+(2A+B). 2a+b)] [x-(a-b)] = 01-(2a+b)1╳-(a-b) So x1= 2a+bx2 = a-b.