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Grade 7 Math Exercise Solutions Page 33 Connecting Knowledge Series is a valuable resource for mastering Polynomial Addition and Subtraction with one variable. Through this material, students will easily understand and solve exercises 7.12, 7.13, 7.14, 7.15, 7.16, and 7.17.
Other Grade 7 Math Resources:
- Grade 7 Math Exercise Solutions Connecting Knowledge with Life Series
- Grade 7 Math Exercise Solutions Page 59 Book 2 of the Kite Series - Exercise 3: Polynomial Addition and Subtraction with one variable
- Grade 7 Math Exercise Solutions Pages 35, 36 Book 2 of the Horizon Series - Exercise 3: Polynomial Addition and Subtraction with one variable
Grade 7 Math Exercise Solutions Page 33 Connecting Knowledge with Life Series
Polynomial Addition and Subtraction with One Variable
1. Solve Exercise 7.12 Page 33 Grade 7 Math Textbook
Problem: Find the sum of the following polynomials by grouping like terms:
Solution Guide:
To add (or subtract) two polynomials, follow these steps:
Step 1: Write down the two polynomials within parentheses.
Step 2: Perform the removal of parentheses (according to the rules of parentheses).
Step 3: Group like terms.
Step 4: Add or subtract like terms.
Answer:
2. Solve Exercise 7.13, Page 33 of Grade 7 Math Textbook
Solution Guide:
Arrange subtraction so that like terms are aligned in columns and then subtract column by column.
Answer:
3. Solve Exercise 7.14, Page 33 of Grade 7 Math Textbook
Solution Guide:
To add (or subtract) two polynomials, follow these steps:
Step 1: Write down the two polynomials within parentheses.
Step 2: Remove parentheses (according to the rules of parentheses).
Step 3: Group like terms.
Step 4: Add or subtract like terms.
Answer:
We have:
4. Solve Exercise 7.15 on Page 33 of Grade 7 Math Textbook
Solution Guide:
To add (or subtract) two polynomials, follow these steps:
Step 1: Write down the two polynomials within parentheses.
Step 2: Perform the removal of parentheses (according to the rules of parentheses).
Step 3: Group like terms.
Step 4: Add or subtract like terms.
Answer:
We have:
5. Solving Exercise 7.16 on Page 33 of Math Textbook Grade 7
Problem Statement: Nam has been assigned to buy some books as gifts for the end-of-year class summary. Nam plans to buy three types of books with the selling prices as shown in the table below. Assuming Nam needs to buy x science books, x + 8 reference books, and x + 5 comic books.
a) Write polynomials representing the amount Nam has to pay for each type of book.
b) Find the polynomial representing the total amount Nam has to pay to buy that number of books.
Solution Guide:
a) Amount Nam has to pay for each type of book = price of each type of book. (number of books Nam needs to buy).
b) Total amount Nam has to pay to buy that book = amount for comic books + amount for reference books + amount for science books.
Answer:
a) The polynomial representing the amount Nam has to pay to buy comic books is: 15000(x + 5).
The polynomial representing the amount Nam has to pay to buy reference books is: 12500(x + 8).
The polynomial representing the amount Nam has to pay to buy science books is: 21500x.
b) The polynomial representing the total amount Nam has to pay to buy that number of books is:
6. Solving Exercise 7.17 on Page 33 of Math Textbook Grade 7
Problem Statement: On a rectangular piece of land with a length of 65 meters, it is planned to build a swimming pool with a width of x meters, the length of which is 3 times the width. The diagram and specific dimensions (measured in meters) are provided in Figure 7.1. Find the polynomial (variable x):
a) Represent the area of the swimming pool.
b) Represent the area of the piece of land.
c) Represent the area of the land surrounding the swimming pool.
Guide:
+ Observe the diagram to determine the length and width of the rectangular piece of land and the swimming pool.
+ Area of the rectangle = length x width.
Answer:
The swimming pool has a width of x (m) and a length of 3x (m).
The piece of land has a width of 9 + x (m) and a length of 65 (m).
a) Area of the swimming pool:
S(x) = 3x^2
b) Area of the land:
P(x) = 65x + 585
c) Area of the land surrounding the swimming pool:
Here is the guide to solving math problems for grade 7, page 33, volume 2. Students should also refer to solving math problems for grade 7, page 35, volume 2, and review solving math problems for grade 7, page 30, volume 2 to ensure understanding.
- Solving math problems for grade 7, page 35, volume 2, Kết Nối Tri Thức - Concentrated exercise on page 34
- Solving math problems for grade 7, page 30, volume 2, Kết Nối Tri Thức - Exercise 25: Polynomial one variable
