The law of multiplication and distribution is a basic law in mathematics, which describes that the sum of two numbers multiplied by a number equals the results of multiplication and addition of these two numbers respectively.

For any two real numbers A and B and any real number C, there is (a+b) × c = a× c+b× c, and it is also very simple to prove this law. We can expand (a+b)×c on the left and get a×c+b×c, which is the same as a×c+b×c on the right, so the two expressions are equal.

Multiplication and distribution law is a universal mathematical law, which is not only applicable to integers and decimals, but also to real numbers such as fractions and negative numbers. Whether in basic mathematics or advanced mathematics, the law of multiplication and distribution is an important concept and has a wide range of application values. At the same time, multiplication and division is also the basis for students to master other mathematical concepts and skills.

Application scenarios of multiplication and distribution law;

1, algebra: in algebra, multiplication and division are often used to decompose factors and simplify expressions. For example, (x+y) (x-y) = x 2-y 2, which is the application of the square difference formula. In addition, multiplication and division can also be used to solve some algebraic problems, such as finding the value of polynomials or solving equations.

2. Geometry: In geometry, the area and volume can be calculated by the law of multiplication and distribution. For example, if the length of a rectangle is a and the width is b, then the area of this rectangle is a× B. If this rectangle is divided into two smaller rectangles, then the sum of the areas of these two small rectangles is equal to the area of the original rectangle.

3. Triangle: In trigonometry, multiplication, division and distribution can be used to calculate angles and radians. For example, sin(a+b)=sinacosb+cosasinb, which is the application of trigonometric function addition theorem.

4. Daily life: In daily life, the law of multiplication and distribution is also widely used. For example, when shopping, calculate the total price of goods. If the unit price of goods is fixed, you only need to multiply the quantity of goods by the unit price to get the total price.

5. Practical problems: In some practical problems, multiplication and division can also be used to solve problems. For example, calculating torque physically, calculating material strength in engineering and so on.