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Giải bài 7 trang 28 vở thực hành Toán 8

Chứng minh rằng với mọi số tự nhiên n, ta có:

𝓰Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Chứng minh rằng với mọi số tự nhiên n, ta có:

ꩲ\({\left( {n + 2} \right)^2}\;-{n^2}\) chia hết cho 4.

Phương pháp giải - Xem chi tiết

💛Sử dụng hằng đẳng thức bình phương của một tổng: \({\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\)

Lời giải chi tiết

ไTa có \({\left( {n + 2} \right)^2}\;-{n^2}\; = \left( {{n^2}\; + 4n + 4} \right)-{n^2}\; = 4n + 4\).

Vì \(4\; \vdots \;4\) nên tích 4n chia hết cho 4.

ꦑVậy \({\left( {n + 2} \right)^2}\;-{n^2}\) chia hết cho 4.

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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