Giải bài tập sách bài tập (SBT) toán lớp 8 chân trời sáng tạo bài Bài tập ôn cuối chương 1

The book "Chân trời sáng tạo" for math exercises in grade 8 contains a variety of creative and challenging exercises. In this article, we will focus on the last exercises from chapter 1, providing detailed solutions and explanations for each question.

Multiple Choice Questions:

We will walk through the solutions for the following multiple-choice questions:

Question 1: Determine the degree of the monomial $2x^{2}y(2y^{2})^{2}$.

Answer: The degree of $8x^{2}y^{5}$ is 7.

Question 2: Find the result of the multiplication $(4x – y)(y + 4x)$.

Answer: The result is $16x^{2} – y^{2}$.

Question 3: Simplify the expression $(a^{2} – 2a + 4)(a + 2)$.

Answer: The result is $a^{3} + 8$.

Question 4: Factor the polynomial $16x^{2} – y^{4}$.

Answer: The factors are $(4x – y^{2})(4x + y^{2})$.

Question 5: Simplify the expression $x^{2}(x + 1) – x(x + 1)$.

Answer: The result is $x(x + 1)(x - 1)$.

Self-Practice Exercises:

We will solve the following exercises independently:

Exercise 11: Simplify the expressions $ab(3a – 2b) – ab(3b – 2a)$ and $(a – 4b)(a + 2b) + a(a + 2b)$.

Answer: The solutions are $5a^{2}b – 5ab^{2}$ and $2a^{2} – 8b^{2}$, respectively.

Exercise 12: Factorize the expressions $(a – 4)(a + 4)$ and $(3a – b)^{2} – (a – 2b)(2b – a)$.

Answer: The factored forms are $a^{2} - 16$ and $10a^{2} – 10ab + 5b^{2}$.

Exercise 13: Perform the calculations $(a + 1 + \frac{1 - 2a^{2}}{a - 1}) : (1 - \frac{1}{1-a})$ and $(\frac{a}{b^{2}} - \frac{1}{a}) : (\frac{1}{b} + \frac{1}{a})$.

Answer: The results are $-a$ and $\frac{a-b}{b}$, respectively.

Exercise 14: Given a figure with specific measurements, find the lengths of various edges and calculate the perimeter.

Answer: The lengths and total perimeter are detailed in the solution.

Exercise 15: Modify the design of a cube-shaped box and determine the changes in volume and surface area.

Answer: The differences in volume and surface area after modification are provided.

Exercise 16: Adjust the measurements of a proposed square box and analyze the effects on volume and perimeter.

Answer: The variations in volume and perimeter due to adjustments are explained.

By following the detailed solutions to these exercises, students can enhance their problem-solving skills and strengthen their understanding of mathematical concepts. Practice is key to mastering mathematics, and these exercises offer a great opportunity for students to apply their knowledge.