First, the classification of algebraic expressions
1, monomial refers to a mathematical expression that only contains multiplication and division operations. For example, 2x and 3y are both monomials. The coefficient of a single item refers to the numerical factor in a single item, for example, the coefficient of 2x is 2; The degree of a monomial refers to the sum of the exponents of all the letters in the monomial, for example, the degree of 2x is 1.
2. Polynomial refers to a mathematical expression composed of multiple monomials. For example, 3x+5y+z are all polynomials. Polynomial terms refer to each monomial that constitutes a polynomial, such as 3x, 5y and z terms in 3x+5y+z; The degree of polynomial refers to the degree of the term with the highest degree in polynomial, for example, the degree of 3x+5y+z is 2.
Second, the operation rules of algebraic expressions
1, the rules of addition, subtraction, multiplication and division in algebraic expressions, the order of addition, subtraction, multiplication and division is multiplication and division first and then addition and subtraction. For example: 2x+3y-4z=2x+(3y-4z).
2. Rules of power operation In algebraic expressions, the order of power operation is power first and then multiplication and division. For example: (-2) 3 =-8.
3. Parenthesis operation rules In algebraic expressions, the order of parenthesis operation is first in parentheses and then outside parentheses. For example: 2(x+y+z)=2x+2y+2z.
The operation of algebraic expressions: coefficient, degree, addition, subtraction, multiplication and division.
1, the coefficient and number of algebraic expressions.
Algebraic expressions are expressions composed of numbers and letters. According to the number of algebraic expressions, we can divide them into monomial and polynomial expressions. The degree of a single term is 1, and the degree of a polynomial refers to the degree of the highest term. The algebraic coefficient refers to the number multiplied by the letter, which can be positive, negative or zero.
1 and the addition and subtraction of algebraic expressions
Addition and subtraction of algebraic expressions refers to the operation of merging and sorting similar items. In algebraic addition and subtraction, we need to find similar items first, and then merge them. For example, for the polynomial 2x? +3x-4x？ +5x, can we find similar items 2x first? And -4x? Then merge to get (2-4)x? +(3+5)x=-2x？ +8 times.
3. Multiplication and division of algebraic expressions.
The multiplication and division of algebraic expression refers to the operation of multiplying or dividing algebraic expression and algebraic expression. In algebraic multiplication and division, we need to follow the operation rules such as multiplication distribution law and multiplication association law. For example, for the polynomial (2x+3)(x-4), we can first expand it to get 2x? -8x+3x- 12=2x？ -5x- 12 .