Real number calculation How much is sin & sup2; 25 ° + Sin & sup2; 65 ° and Sin & sup2; 20 ° + Sin & sup2; 70?, the reason is more detailed What does that & sup2; mean? I know it's Square

Real number calculation How much is sin & sup2; 25 ° + Sin & sup2; 65 ° and Sin & sup2; 20 ° + Sin & sup2; 70?, the reason is more detailed What does that & sup2; mean? I know it's Square

sin²25°+sin²65°=1
sin²20°+sin²70°=1
Because 25 + 65 = 20 + 70 = 90
So both = 1
&Sup2; is the square

Take the equation 5-2 / 1 + 2x = 1 and remove the denominator
one
It's a project

5-1/2+2x=1
The two sides of the equal sign are multiplied by two to get
10-1+4x=2

Equation 2x + 32-x = 9x-53 + 1 gets ()
A. 3（2x+3）-x=2（9x-5）+6B. 3（2x+3）-6x=2（9x-5）+1C. 3（2x+3）-x=2（9x-5）+1D. 3（2x+3）-6x=2（9x-5）+6

By multiplying both sides of the equation 2x + 32-x = 9x-53 + 1 by 6, we can get 3 (2x + 3) - 6x = 2 (9x-5) + 6

How to solve the equation with denominator x
RT column as (1.6x + 0.55x) / x = 0.7 to say the concept is better
How to solve the quadratic equation of one variable, that is, there are several solutions for 2x ^ 2-3x + 1 = 0, why

The equation in your example has no solution
When x is 0, both sides are equal, but the denominator cannot be 0, so the equation has no solution

The denominator of the equation x / 2-x-1 / 6 = 1 is removed as ()

3X/6-(X-1)/6=1
(3X-(X-1))/6=1
2X-1=6
2X=7
X=3.5

Factorization and definition of factorization
Please be accurate

Factorization is a noun
Factorization is a verb

What is the function of factorization?
If the function is to simplify, then why can't there be fractions?
Is it because I don't know if the unknown is zero?

The problems of algebra in middle school can be summarized into four categories: calculation, evaluation, simplification and demonstration. The key to solving the problems of algebra is to make the algebra identical deformation through algebraic operation. One of the important means of the identical deformation of algebra is factorization, which runs through and permeates all kinds of problems of algebra
Factorization is based on the study of the four operations of rational number and integral. It provides the necessary basis for the later study of fractional operation, solving equations and equations, and the identical transformation of algebraic and trigonometric functions. Therefore, factorization is an important content of algebra textbooks for middle school. It has a wide range of basic knowledge functions
Because of the flexible and comprehensive use of the basic knowledge of mathematics in factoring, there are many ways to factoring and strong skills, so reverse thinking has a certain depth and breadth for middle school students, So factorization is a good carrier to develop students' intelligence, cultivate their ability and deepen their reverse thinking. Just because factorization has a good function of cultivating their ability and thinking, factorization is also a difficult point in algebra textbooks for middle school
The content of factorization in this chapter is part of the most basic knowledge and methods of factorization of polynomials. It includes the related concepts of factorization, the differences and relations between integral multiplication and factorization, and four basic methods of factorization, namely, the method of quoting common factor, the method of using formula, the method of grouping factorization and the method of cross multiplication. Finally, the general steps of factorization are summarized and given
Factorization of polynomials is an important part of algebraic formulas. It is closely related to the integral in the previous chapter and the fraction in the latter chapter. The teaching of factorization is based on the four operations of integral, The theoretical basis of factorization method is the inverse transformation of polynomial multiplication. This part has direct application in the general division and reduction of fractions. Factorization is also often used in solving equations and the identical transformation of trigonometric functions. Therefore, enough attention should be paid to this part in teaching
The concept of factorization is to transform a polynomial into the product of several integers. In the introduction of the textbook, this concept is explained in combination with the illustrations in front of this chapter. It can also be explained by analogy with the concept of factorization in primary school mathematics. In teaching, students should not be required to thoroughly understand the concept of factorization at one time, but should be taught the four basic methods of factorization, Combined with the decomposition process and results of specific examples, the significance of the concept is explained, so as to achieve the teaching purpose of gradually understanding the concept
The common factor method is the most basic and common method of factorization. Its theoretical basis is the distributive law of multiplication. Using this method, we should first investigate the polynomial to be decomposed, and propose the common factor of letter coefficient and the highest common factor of common letter or common factor
About the use of formula method, the textbook tells the most commonly used five formulas. The key to using formula method is to be familiar with the form and characteristics of each formula. For beginners, it is not easy to choose which formula should be used according to the form and characteristics of the polynomial to be decomposed. This is also the difficulty of using formula method, In order to overcome the difficulties
The grouping decomposition method is the comprehensive application of the first two methods. There are two types in the textbook. One is that the common factor can be directly proposed after grouping, and the other is that the formula can be used after grouping. Due to the different forms of polynomials, the grouping methods are also different. It is necessary to analyze the specific problems and foresee the possibility of decomposing the whole polynomial after grouping, The group decomposition method is more difficult than the former two methods. In teaching, according to the level of the teaching material, the first is easy, the second is difficult, and the last is a slightly comprehensive factorization topic
Cross multiplication is a method suitable for decomposing some quadratic trinomials. The textbook arranges this part in two levels. The first part is the case that the coefficient of the quadratic trinomial is 1, and the second part is the case that the coefficient of the quadratic trinomial is not 1, In teaching, we should strictly control the teaching requirements, do not increase the content and improve the requirements at will
At the end of this chapter, the contents of factoring polynomials with the above four methods are arranged. The teaching of this part should be analyzed according to different topics, and various methods should be flexibly used to decompose factors. This part is the difficulty of teaching. It should be arranged according to the teaching requirements and students' learning level, and should not be too high
The general steps of factorization are described after summarizing all kinds of factorization methods. In teaching, it is necessary to select and determine which method to use according to the form and characteristics of the topic. The four methods are related to each other, not one type of polynomial, so only one method can be used to decompose the factor. In teaching, students should learn how to analyze specific problems
New knowledge points
(1) Factoring a polynomial into the product of several integers is called factoring the polynomial or factoring the polynomial
(2) Common factor: each term of a polynomial contains the same factor, which is called the common factor of the polynomial
(3) The method to determine the common factor: the coefficient of the common factor should be the greatest common divisor of each coefficient; the letter should be the same letter of each item, and the index of each letter should be the lowest
(4) Common factor method: in general, if each item of a polynomial has a common factor, the common factor can be mentioned outside the brackets, and the polynomial can be written in the form of factor product. This method of factoring is called common factor method
(5) After putting forward the common factor of polynomial, another way to determine the factor is to divide the original polynomial by the common factor, and the quotient obtained is another factor
(6) If the coefficient of the first term of a polynomial is negative, it is generally necessary to put forward the sign of "-" so that the coefficient of the first term in brackets is positive. When the sign of "-" is put forward, all items of the polynomial will change sign
(7) The relationship between factorization and integral multiplication: Factorization and integral multiplication are positive and negative processes of integral identity transformation, the result of integral multiplication is integral, and the result of factorization is product
(8) Using formula method: if the multiplication formula is reversed, it can be used to factorize some polynomials. This factorization method is called using formula method
(9) Square difference formula: the square difference of two numbers is equal to the sum of the two numbers multiplied by the difference of the two numbers. Letter expression: A2-B2 = (a + b) (a-b)
(10) What characteristics of binomial formula can be used to decompose the factor
① The coefficient can be squared
② The letter index should be in pairs
③ The two signs are opposite
(11) The key of factoring with the square difference formula is to write each term in the form of square and correctly judge what a and B are equal to
(L2) complete square formula: the sum of the squares of two numbers, plus (or minus) two times the product of the two numbers, is equal to the square of the sum (or difference) of the two numbers
(13) The characteristics of the complete square formula are as follows
① It is a trinomial
② Two of them are the sum of the squares of some two numbers
③ The third term is the positive or negative double of the product of the two numbers
④ With the above three characteristics, it is equal to the square of the sum (or difference) of the two numbers
(14) The formula of cubic sum and cubic difference: the cubic sum (or difference) of two numbers is equal to the sum (or difference) of the two numbers multiplied by the difference (or sum) of their square sum and their product
(15) The key to the factorization of cubic sum and cubic difference is to be able to write these two terms in the form of some two number cube
(16) If the terms of a polynomial are grouped and a common factor is proposed, the factorization can be continued among the groups, then the polynomial can be factorized by the grouping decomposition method
(17) The premise of group decomposition: Mastering the common factor method and formula method is the premise of learning group decomposition well
(18) The principle of grouping decomposition method: after grouping, the common factor can be put forward directly, or the formula can be used directly after grouping
(19) When grouping, whether factorization can be continued after grouping should be considered in advance
(20) For a general form of quadratic trinomial x2 + PX + Q with quadratic coefficient 1, if the constant term q is decomposed into two factors A and B, and a + B is equal to the coefficient P of the first term, then it can be decomposed into factors
That is, X2 + PX + q = x2 + (a + b) x + ab
=(x+a)(x+b)
The key here is to master the relationship between a, B and the coefficients of the constant term and the first-order term of the original polynomial, which is mainly: ab = q, a + B = P
(21) cross multiplication: a method of factoring quadratic trinomials by drawing cross lines to decompose coefficients
(22) cross multiplication factorization: mainly used for Factorization of some quadratic trinomials
(23) for a quadratic trinomial AX2 + BX + C whose coefficient of quadratic term is not 1 in general form, the key to decomposing the factor by cross multiplication is to find out four factors such as A1A2 = a, C1C2 = C, a1c2 + a2c1 = B
In order to reduce the number of attempts and simplify the sign problem, when the coefficient of the quadratic term is negative, the negative sign should be put forward to make the coefficient of the quadratic term positive. When the coefficient of the quadratic term is decomposed into a factor, only the product of two positive numbers should be considered
That is, AX2 + BX + C = a1a2x2 + (a1c2 + a2c1) x + C1C2
＝(a1x＋c1)(a2x＋c2)
(24) the necessary and sufficient condition of factoring quadratic trinomial AX2 + BX + C is that b2-4ac is the square of a rational number
(25) general steps of factorization:
① If each term of a polynomial has a common factor, the common factor is first mentioned;
② If there is no common factor, try to use it