Eighth grade math mind map: congruent triangles eighth grade math mind map: quadratic form eighth grade math mind map: real number eighth grade math mind map: factorization of similar graphics eighth grade math mind map 1. Factorization of a polynomial into several algebraic expressions is called factorization of this polynomial. Note: Factorization and multiplication are two opposite transformations.
2. Factorization method: commonly used? Extraction of common factors? 、? Formula method? 、? Group decomposition? 、? Cross multiplication? .
3. Determination of common factor: What is the greatest common factor of the coefficient? The lowest power of the same factor.
Pay attention to the formula: a+b = b+a; a-b =-(b-a)； (a-b)2 =(b-a)2； (a-b)3=-(b-a)3。
4. The formula of factorization:
(1) square difference formula: A2-B2 = (a+b) (a-b);
(2) Complete square formula: A2+2ab+B2 = (a+b) 2, A2-2ab+B2 = (a-b) 2.
5. Matters needing attention in factorization:
(1) The general order of selecting factorization methods is: one extraction, two formulas, three grouping and four crossover;
(2) When using factorization formula, special attention should be paid to the integrity of letters in the formula;
(3) The final result of factorization needs factorization until every factorization cannot be decomposed;
(4) The final result of factorization requires the first sign of each factor to be positive;
(5) The final result of factorization needs to be sorted;
(6) The final result of factorization requires that the same factor be written as a power.
6. Problem solving skills of factorization: (1) transposition arrangement, bracket arrangement or bracket arrangement; (2) negative sign; (3) Total symbol change; (4) exchange RMB; (5) formula; (6) treating the same formula as a whole; (7) flexible grouping; (8) extracting the fractional coefficient; (9) expand some or all of the brackets; (10) Dismantle or supplement.
7. Completely flat mode: A polynomial that can be reduced to (m+n)2 is called completely flat mode; Is there a quadratic trinomial x2+px+q? X2+px+q is completely flat.
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1. Fraction: A and B are generally used to represent two algebraic expressions, A? B can be expressed as. If b contains letters, the formula is called a fraction.
2. Rational formula: Algebraic formula and fractional formula are collectively called rational formula; Namely.
3. Two important judgments about the score: (1) If the denominator of the score is zero, the score is meaningless, and vice versa; (2) If the numerator of a fraction is zero and the denominator is not zero, the value of the fraction is zero; Note: If the numerator of a fraction is zero and the denominator is zero, the fraction is meaningless.
4. The basic nature and application of scores;
(1) If both the numerator and denominator of a fraction are multiplied by (or divided by) the same non-zero algebraic expression, the value of the fraction remains unchanged;
(2) Note: In a fraction, if any two symbols of numerator, denominator and fraction itself are changed, the value of the fraction remains unchanged;
that is
(3) When simplifying the complex fraction, it is relatively simple to multiply the numerator denominator by the least common multiple of the decimal denominator.
5. Fraction: The divisor of the numerator and denominator of a fraction is called a fraction; Note: Factorization is often needed before fractional reduction.
6. simplest fraction: There is no common factor between the numerator and denominator of a fraction. This fraction is called simplest fraction; Note: The final result of score calculation requires simplification to the simplest score.
7. The law of multiplication and division of scores:
8. the power of the score:.
9. The calculation rules of negative integral index:
(1) formula: a0= 1(a? 0)，a-n= (a？ 0);
(2) The algorithm of positive integer exponent can be used to calculate negative integer exponent;
(3) Formula:
(4) Formula: (-1)-2 = 1, (-1)-3 =- 1.