Buzz
Solutions to exercises 1 through 9 in the textbook on Polynomial Addition and Subtraction are extensively elucidated in the document for Solving Math problems for 7th grade from pages 35 and 36 of Workbook 2 from the book 'Creative Horizon Mathematics'. Students and teachers teaching Grade 7 Mathematics are encouraged to refer to it for optimal exercise preparation.
Other recommended Math study materials:
- Solving Math problems for 7th grade from the book 'Creative Horizon Mathematics'
- Solving Math problems for 7th grade from pages 30 of Workbook 2 from the book 'Knowledge Connection' - Lesson 25: Polynomial with One Variable
- Solving Math problems for 7th grade from pages 52 and 53 of Workbook 2 from the book 'Kite' - Exercise 2: Polynomial with One Variable. Solutions of Polynomial with One Variable
Solving Math problems for 7th grade from pages 35 and 36 of Workbook 2 from the book 'Creative Horizon Mathematics'
Addition and Subtraction of Polynomials with One Variable
1. Solving Exercise 1 Page 35 of Grade 7 Math Textbook
Guidelines for solving:
To add (subtract) two polynomials with one variable, we can perform one of the following two methods:
Method 1: Group the monomials with the same variable exponents and then perform addition (subtraction).
Method 2: Arrange the monomials of the two polynomials in order of increasing (or decreasing) exponents of the variable and align them vertically so that the same exponent in the two polynomials is in the same column, then perform addition (subtraction) vertically.
Answer:
We have:
2. Solving Exercise 2 Page 35 Grade 7 Math Textbook
3. Solving Exercise 3 Page 36 Grade 7 Math Textbook
4. Solving Exercise 4 Page 36 Grade 7 Math Textbook
Problem: Write an expression representing the perimeter of an isosceles trapezoid in Figure 3.
Solution Guide:
The perimeter of a trapezoid is equal to the sum of the lengths of its sides.
Answer:
The expression representing the perimeter of the isosceles trapezoid in the figure above is:
8x + 4x + 1 + 16x - 6 + 4x + 1 = 32x - 4
5. Solving Exercise 5 Page 36 Grade 7 Math Textbook
Problem: In triangle (Figure 4) with a perimeter of 12t - 3. Find the unknown side of the triangle.
Solution Guide:
The perimeter of a triangle is equal to the sum of the lengths of its sides.
To find the unknown side, subtract the sum of the two known sides from the perimeter.
Answer:
We have:
12t - 3 - (3t + 8) - (4t - 7) = 12t - 3 - 3t - 8 - 4t + 7 = 5t - 4.
So the unknown side of the triangle is: 5t - 4.
6. Solving Exercise 6 Page 36 Grade 7 Math Textbook
Problem: Given three polynomials:
Calculate P(x) + Q(x) + R(x) and P(x) - Q(x) - R(x).
Solution Guide:
To add (subtract) two polynomials with one variable, we can perform one of the following two methods:
Method 1: Group the monomials with the same variable exponents and then perform addition (subtraction).
Method 2: Arrange the monomials of the two polynomials in order of increasing (or decreasing) exponents of the variable and align them vertically so that the same exponent in the two polynomials is in the same column, then perform addition (subtraction) vertically.
Answer:
7. Solving Exercise 7 Page 36 Grade 7 Math Textbook
Solution Guide:
Write the polynomial P(x) as the sum of a fourth-degree polynomial such that the sum of the coefficients of the fourth-degree terms is 0. The sum of the coefficients of the remaining terms equals the coefficient of the corresponding term in P(x).
Answer:
There are many ways to write this problem. Here's an example of one way to write it.
8. Solving Exercise 8 Page 36 Grade 7 Math Textbook
Problem: Given a square with side length 2x and inside is a rectangle with side lengths x and 3 (Figure 5).
Find the polynomial in terms of variable x representing the area of the shaded region.
Solution Guide:
Area of the shaded region = Area of the square - Area of the rectangle.
Answer:
The area of the shaded region is: (2x)2 - 3x = 4x2 - 3x.
So the polynomial in terms of variable x representing the area of the shaded region is: 4x2 - 3x.
9. Solving Exercise 9 Page 36 Grade 7 Math Textbook
Problem: a) Perform the operation: (3x - 1) + [(2x2 + 5x) + (4 - 3x)].
b) Given A = 4x + 2, C = 5 - 3x2. Find the polynomial B such that A + B = C.
Solution Guide:
a) Use the bracket rule, expand and perform operations within the square brackets first.
b) A + B = C. Hence, B = C - A.
Answer:
Here is the guidance for Grade 7 Math solving on pages 35, 36 Workbook 2. Students, please refer to Grade 7 Math solving on pages 40 and 42 Workbook 2 first and review Grade 7 Math solving on pages 31, 32 Workbook 2 to ensure understanding.
- Grade 7 Math solving on page 40 Workbook 2 'Creative Horizon Mathematics' - Exercise 4: Multiplication and division of polynomials with one variable
- Grade 7 Math solving on page 42 Workbook 2 'Creative Horizon Mathematics' - End of chapter 7 exercises
