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Giải bài 1 trang 39 Chuyên đề học tập Toán 10 – Chân trời sáng tạo

Khai triển biểu thức:

Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạ🌱o

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Đề bài

Khai triển biểu thức: a) \({(x - 2y)^6}\) b) \({(3x - 1)^5}\)

Phương pháp giải - Xem chi tiết

Sử dụng công thức nhị thức Newton \({(a + b)^n} = C_n^0{a^n} + C_n^1{a^{n - 1}}b + ... + C_n^{n - 1}a{b^{n - 1}} + C_n^n{b^n}\) hoặc tam giác Pascal

Lời giải chi tiết

a) Sử dụng tam giác Pascal, ta có: \(\begin{array}{l}{(x + ( - 2y))^6} = {x^6} + 6{x^5}( - 2y) + 15{x^4}{( - 2y)^2} + 20{x^3}{( - 2y)^3} + 15{x^2}{( - 2y)^4} + 6x{( - 2y)^5} + {( - 2y)^6}\\ = {x^6} - 12{x^5}y + 60{x^4}{y^2} - 160{x^3}{y^3} + 240{x^2}{y^4} - 192x{y^5} + 64{y^6}\end{array}\) b) Sử dụng tam giác Pascal, ta có: \(\begin{array}{l}{(3x - 1)^5} = {\left( {3x} \right)^5} + 5.{\left( {3x} \right)^4}( - 1) + 10.{\left( {3x} \right)^3}{( - 1)^2} + 10.{\left( {3x} \right)^2}{( - 1)^3} + 5.\left( {3x} \right){( - 1)^4} + {( - 1)^5}\\ = 243{x^5} - 405{x^4} + 270{x^3} - 90{x^2} + 15x - 1\end{array}\)  

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