Factorization 1. In factorization, if there is a common factor, the common factor is first extracted and then further decomposed.
2. Factorization must be carried out until each polynomial factor can no longer be decomposed.
Perfect square trinomial
(1) Reversing the multiplication formula (a+b)2=a2+2ab+b2 and (a-b)2=a2-2ab+b2, we can get:
a2+2ab+b2=(a+b)2
a2-2ab+b2=(a-b)2
That is to say, the sum of squares of two numbers, plus (or minus) twice the product of these two numbers, is equal to the square of the sum (or difference) of these two numbers.
Equations a2+2ab+b2 and a2-2ab+b2 are called completely flat modes.
The above two formulas are called complete square formulas.
(2) the form and characteristics of completely flat mode
① Number of projects: three projects.
② Two terms are the sum of squares of two numbers, and the signs of these two terms are the same.
A term is twice the product of these two numbers.
(3) When there is a common factor in the polynomial, the common factor should be put forward first, and then decomposed by the formula.
(4) A and B in the complete square formula can represent monomials or polynomials. Here as long as the polynomial as a whole.
(5) Factorization must be decomposed until every polynomial factor can no longer be decomposed.
After congruent triangles (1) flips and translates, two triangles that can completely overlap are called congruent triangles, and the three sides and three angles of the two triangles are equal.
(2) The nature of congruent triangles
1. The angles corresponding to congruent triangles are equal.
2. The corresponding sides of congruent triangles are equal.
3. Vertices that can completely coincide are called corresponding vertices.
4. The heights of the corresponding sides of congruent triangles are equal.
5. The bisectors of the corresponding angles of congruent triangles are equal.
6. The median lines of the corresponding sides of congruent triangles are equal.
7. congruent triangles is equal in area and circumference.
8. The trigonometric functions of congruent triangles corresponding angles are equal.
(3) congruent triangles's judgment
(1)SSS (side by side)
A triangle with three equal sides is congruent triangles.
(2)SAS (edge)
A triangle with two equal corners is congruent triangles.
(3)ASA (corner)
Two angles and their sides correspond to congruences of triangles.
(4)AAS (corner)
The opposite sides of two angles and one angle correspond to congruences of equal triangles.
(5)RHS (right angle, hypotenuse, edge)
In a pair of right-angled triangles, the hypotenuse is equal to the other right-angled side.
The formula of angle correlation theorem 1 is equal to the complementary angle and two straight lines are parallel.
2. The internal dislocation angles are equal and the two straight lines are parallel.
3. The internal angles on the same side are complementary and the two straight lines are parallel.
4. Two straight lines are parallel and have the same angle.
5. The two straight lines are parallel and the internal dislocation angles are equal.
6. These two straight lines are parallel and complementary.
7. Theorem 1 The distance between a point on the bisector of an angle and both sides of the angle is equal.
8. Theorem 2 The point where two sides of an angle are equidistant is on the bisector of this angle.
9. The bisector of an angle is the set of all points with equal distance to both sides of the angle.
A binary linear equation contains two unknowns, and the degree of the unknowns is 1, which is called a binary linear equation.
Binary linear equations: The equations composed of two binary linear equations are called binary linear equations.
A set of unknown values suitable for binary linear equation is called the solution of this binary linear equation.
The common * * * solution of each equation in a binary linear system of equations is called the solution of this binary linear system of equations.
Methods of solving binary linear equations: substitution elimination method/addition and subtraction elimination method.
Inequality and inequality group (1) inequality
Using inequality symbols (
(2) the essence of inequality
① symmetry;
② Transitivity;
③ monotonicity of addition, that is, additivity of inequality in the same direction;
④ Monotonicity of multiplication;
⑤ Multiplicity of positive inequality in the same direction;
⑥ Positive inequalities can be multiplied;
⑦ Positive inequalities can be squared;
(3) One-dimensional linear inequality
A formula connected by an inequality symbol contains an unknown number whose degree is 1, whose coefficient is not 0, and whose left and right sides are algebraic expressions is called one-dimensional linear inequality.
(4) One-dimensional linear inequalities
The group of one-dimensional linear inequalities consists of several one-dimensional linear inequalities with the same unknowns.
Algebra 1. Algebraic expression: the expression of the number of connections, and the letter indicating the number with the operation symbol "+-×××" is called algebraic expression (the number obtained by the letter should ensure that the formula in which it is located is meaningful, and the number obtained by the letter should also make real life or production meaningful; A single number or letter is also algebraic)
2. Some points for attention in column algebra:
Multiply (1) by letters, or multiply letters by letters, or omit;
(2) When the numbers are multiplied, they should still be multiplied by "×", but not by "×", and the multiplication sign cannot be omitted;
(3) When a number is multiplied by a letter, the number is usually written in front of the letter in the result. For example, a×5 should be written as 5a;
(4) When the band fraction is multiplied by letters, the band fraction should be changed to a false fraction, for example, a× should be written as a;
(5) When there is a division operation in the algebraic expression, the division method and the division method are generally connected by a fractional line, such as the form written in 3 A;
(6) The difference between A and B should be written in alphabetical order; If we only talk about the difference between two numbers, when we set the two numbers as A and B respectively, we should classify them and write them as a-b and B-A. ..