1, the concept of algebraic expression
Algebraic expressions are general terms for monomials and polynomials. A monomial is a formula composed of the product of numbers and letters, and a polynomial is a formula composed of monomials. In this chapter, we learned how to simplify and calculate algebraic expressions.
2. The essence of algebraic expressions
Algebraic expressions have some special properties, which are very useful in subsequent operations. For example, the multiplication of algebraic expressions satisfies the distribution law, that is, A (B+C) = AB+AC; The division of algebra satisfies the inverse distribution law, that is, A ÷ (B+C) = A ÷ B+A ÷ C. In addition, we also learned how to simplify and deform by using the properties of algebra.
3. Algebraic expression operation
The operations of algebraic expressions include addition, subtraction, multiplication, division and multiplication. In addition and subtraction, we need to pay attention to the combination of similar items; In multiplication, we need to pay attention to the application of distribution law; In division, we need to pay attention to the use of reciprocal; In power, we need to pay attention to the meaning of indicators. Through these basic operations, we can solve some practical problems, such as calculating area and volume.
4. The application of algebraic expressions
The last part of this chapter introduces the application of algebraic expressions, such as solving practical problems, designing and optimizing schemes. These applications can help us better understand the meaning and value of algebraic expressions and improve our mathematical literacy and application ability.
Calculation skills of algebraic expressions;
1, master the algorithm.
In algebraic calculation, we must first master the algorithm. Algebraic addition, subtraction, multiplication and division all have clear arithmetic rules, which need to be carefully studied and mastered. Especially multiplication and division, we need to pay attention to some details and error-prone points.
2. Rational application of the distribution law
Distribution law is a very important property in multiplication of algebraic expressions. It allows us to calculate the results faster. For example, when calculating a(b+c), we can calculate ab and ac first, and then add them to get the result. This can avoid some repeated calculations and improve the calculation efficiency.
3. Flexible use of common factor method.
Common factor method is an important skill in algebraic expression multiplication. By extracting the common factor, we can transform a polynomial into the product of several monomials, which is easier to simplify and deform. For example, in calculating (a+b)(a? B), we can extract a and b respectively, and get a(a? b)+b(a？ B), and then calculate.
4. Pay attention to symbols and brackets
When calculating algebraic expressions, you need to pay attention to symbols and parentheses. Especially for polynomial operations, it is necessary to calculate the contents in brackets first, and then calculate the parts outside brackets. At the same time, we need to pay attention to the change of symbols and the order of operations to avoid wrong results.