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"Merge similar terms" Integers and their addition and subtraction PPT courseware
Xiao Ming provided the following design plan for a rectangular entertainment venue, in which the area outside the semicircular rest area and rectangular swimming area is green space.
(1) What is the area of the swimming area and rest area?
(2) What is the area of green space?
(1) A train travels at a constant speed of v kilometers/hour. The distance traveled by the train after 1.5 hours is 1.5v kilometers;
(2) The base radius of the cone is r, the height is h, and the volume of this cone is 1/3πr²h;
(3) As shown in the picture below, a rectangular box is close to the corner. Its length, width, and height are a, b, and c respectively. The exposed surface area of the box is ab + bc + ca.
summary:
Ask students to review what knowledge they learned in this lesson
This lesson mainly studies the terms and coefficients of algebraic expressions, paying special attention to the symbols they contain.
review:
1. Distributive law of multiplication; (a + b)c = ac + bc
2. What are the terms and coefficients of algebraic expressions; for example: a3-3a2b+3ab2-b3; -15a2b; -2x2y+3y-x.
3. Example: The rectangle in the picture on the right is composed of two small rectangles. Find the area of this rectangle.
There are two representation methods: 8n+5n or (8+5)n
What did you observe from the two algebraic expressions above? What conclusion can you draw?
The concept of similar items:
Concept: Terms that contain the same letters and have the same exponent are called homogeneous terms.
Note: (1) Judging whether similar items have two conditions, both of which are indispensable;
(2) Similar terms have nothing to do with coefficients or the arrangement of letters;
(3) Several constant terms are also similar terms.
For example: (1)2x2y and 5x2y
(2)2ab3 and 2a3b
(3)4abc and 2ab
(4)3mn and -nm
(5)53 and a3
(6)-5 and +3
Merging similar items:
(1) The concept of merging similar items:
Combining similar terms in algebraic expressions into one term is called combining similar terms.
(2) Rules for merging similar items:
The coefficients of similar terms are added, and the result is used as the coefficient, with the letters and their exponents unchanged.
(3) Steps to merge similar items:
The first step is to accurately find similar items (underline them);
The second step is to use the distributive law inversely, and add the coefficients of similar items together (using parentheses), and the letters and their exponents remain unchanged;
Step 3: Write the merged results.
Variation 1. Combine similar items: (a-b)2-3(a-b)-2(a-b)2+7(a-b)
Variation 2. Known: a+b= - ¼ Find the value of the algebraic expression 3(a+b)-5a-5b+7
Variation 3. If the value of the algebraic expression 2y2+3y+7 is 8, find the value of the algebraic expression 4y2+6y-9.
When merging similar items, please note:
1. During the merging process of similar items, the letters and their exponents remain unchanged. Items that are not of the same type cannot be merged.
2. When finding the value of an algebraic expression, you can first combine similar terms to simplify the algebraic expression, and then substitute it into numerical calculations, which often simplifies the calculation process.
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"Merge similar items" PPT courseware 4:
"Combining Similar Terms" PPT Courseware 4 Mathematics exists everywhere in life. Things with the same characteristics can be classified into one category. In polynomials, terms with the same characteristics can also be classified into one category and then combined. Question 1: Above What terms are there in the polynomial of ? 3x2,..
"Merge similar items" PPT courseware 3:
"Combining Similar Items" PPT Courseware 3 Display Activity 1: What are similar items? Display requirements: 1. Accurately explain the concept of similar items; 2. Give some examples of similar items, which must be representative. Let our judgment be more accurate 1. Two are the same: the letters are the same, the same letters refer to...
"Merge similar items" PPT courseware 2:
"Combining Similar Terms" PPT Courseware 2 Independent Exploration: 1. Observe the following monomials, classify the formulas that you think are of the same type, and state the basis for classification -7ab, 2x, 3, 4ab2, 6ab, 0.6ab2, -3x -4.5 Classification basis: Containing the same letters, similar...