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Giải mục 2 trang 20 SGK Toán 8 tập 1– Chân trời sáng tạo

a) Từ Hình 3a, người ta cắt ghép tạo thành Hình 3b. Viết hai biểu thức khác nhau, mỗi biểu thức biểu thị diện tích (phần tô màu) của một trong hai hình bên

Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Châ💜n trờ✨i sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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HĐ2

Video hướng dẫn giải

a) Từ Hình 3a, người ta cắt ghép tạo thành Hình 3b. Viết hai biểu thức khác nhau, mỗi biểu thức biểu thị diện tích (phần tô màu) của một trong hai hình bên.

 

b) Thực hiện phép nhân và rút gọn đa thức, biến đổi biểu thức \(\left( {a + b} \right)\left( {a - b} \right)\) thành một đa thức thu gọn. Từ đó, có kết luận gì về diện tích của hai hình bên?

Phương pháp giải:

a) Áp dụng công thức tính diện tích hình vuông b) Áp dụng công thức tính diện tích hình chữ nhật, quy tắc nhân đa thức.

Lời giải chi tiết:

a) Diện tích Hình 3a là: \({a^2} - {b^2}\) Diện tích Hình 3b là: \(\left( {a + b} \right)\left( {a - b} \right)\) b) Ta có: \(\left( {a + b} \right)\left( {a - b} \right) = a.a - ab + ba - {b^2} = {a^2} - ab + ab - {b^2} = {a^2} - {b^2}\) Suy ra: \(\left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}\) Vậy diện tích của hai hình bằng nhau.

Thực hành 4

Video hướng dẫn giải

Thực hiện các phép nhân: a) \(\left( {4 - x} \right)\left( {4 + x} \right)\)                                    b) \(\left( {2y + 7z} \right)\left( {2y - 7z} \right)\)                       c) \(\left( {x + 2{y^2}} \right)\left( {x - 2{y^2}} \right)\)

Phương pháp giải:

Áp dụng hằng đẳng thức: Hiệu của hai bình phương.

Lời giải chi tiết:

a) \(\left( {4 - x} \right)\left( {4 + x} \right) = {4^2} - {x^2} = 16 - {x^2}\) b) \(\left( {2y + 7z} \right)\left( {2y - 7z} \right) = {\left( {2y} \right)^2} - {\left( {7z} \right)^2} = 4{y^4} - 49{z^2}\) c) \(\left( {x + 2{y^2}} \right)\left( {x - 2{y^2}} \right) = {x^2} - {\left( {2{y^2}} \right)^2} = {x^2} - 4{y^4}\)

Thực hành 5

Video hướng dẫn giải

Tính nhanh: a) \(82.78\)                                           b) \(87.93\)                              c) \({125^2} - {25^2}\)

Phương pháp giải:

Đưa tích của hai thừa số về dạng tích của một tổng và một hiệu rồi áp dụng hằng đẳng thức: Hiệu của hai bình phương.

Lời giải chi tiết:

a) \(82.78 = \left( {80 + 2} \right)\left( {80 - 2} \right) = {80^2} - {2^2} = 6400 - 4 = 6396\) b) \(87.93 = \left( {90 - 3} \right)\left( {90 + 3} \right) = {90^2} - {3^2} = 8100 - 9 = 8091\) c) \({125^2} - {25^2} = \left( {125 + 25} \right)\left( {125 - 25} \right) = 150.100 = 15000\)

Vận dụng 2

Video hướng dẫn giải

Giải đáp câu hỏi ở đầu bài (trang 18)

Phương pháp giải:

Áp dụng hằng đẳng thức: Hiệu của hai bình phương

Lời giải chi tiết:

Ta có: \({65^2} - {35^2} = \left( {65 + 35} \right)\left( {65 - 35} \right) = 100.30 = 3000\) \(102.98 = \left( {100 + 2} \right)\left( {100 - 2} \right) = {100^2} - {2^2} = 10000 - 4 = 9996\)

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