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Giải bài 8 trang 11 sách bài tập toán 8 - Cánh diều

Cho hai đa thức: (A = {x^7} - 4{x^3}{y^2} - 5xy + 7;B = {x^7} + 5{x^3}{y^2} - 3xy - 3)

ꦬTổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Cho hai đa thức: \(A = {x^7} - 4{x^3}{y^2} - 5xy + 7;B = {x^7} + 5{x^3}{y^2} - 3xy - 3\) a) Tìm đa thức \(C\) sao cho \(C = A + B\) b) Tìm đa thức \(D\) sao cho \(A + D = B\)

Phương pháp giải - Xem chi tiết

Áp dụng phương pháp cộng hai đa thức và trừ hai đa thức để tính đa thức \(C\) và \(D\).

Lời giải chi tiết

a) Ta có:\(\begin{array}{l}C = A + B = \left( {{x^7} - 4{x^3}{y^2} - 5xy + 7} \right) + \left( {{x^7} + 5{x^3}{y^2} - 3xy - 3} \right)\\ = \left( {{x^7} + {x^7}} \right) + \left( { - 4{x^3}{y^2} + 5{x^3}{y^2}} \right) + \left( { - 5xy - 3xy} \right) + 7 - 3\\ = 2{x^7} + {x^3}{y^2} - 8xy + 4\end{array}\)b) Ta có:\(\begin{array}{l}D = B - A\\ = \left( {{x^7} + 5{x^3}{y^2} - 3xy - 3} \right) - \left( {{x^7} - 4{x^3}{y^2} - 5xy + 7} \right)\\ = \left( {{x^7} - {x^7}} \right) + \left( {5{x^3}{y^2} + 4{x^3}{y^2}} \right) + \left( { - 3xy + 5xy} \right) - 3 - 7\\ = 9{x^3}{y^2} + 2xy - 10\end{array}\)

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