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Giải bài 1.16 trang 13 SGK Toán 8 - Cùng khám phá

Cho hai đa thức
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Đề bài

Cho hai đa thức \(A = {x^2} - 3xy + 2{y^2}\)và \(B = {y^2} + 2xy + {x^2} + 1\) a)     Tìm đa thức \(C\) sao cho \(C = A + B\) b)    Tìm đa thức \(D + A = B\)

Phương pháp giải - Xem chi tiết

a)  Viết biểu thức\(C = A + B\) bỏ ngoặc Sắp xếp các đơn thức đồng dạng về cùng một nhóm Cộng, trừ các đơn thức đồng dạng trong mỗi nhóm. b) Biến đổi để tìm biểu thức \(D\) Làm tương tự ý a.

Lời giải chi tiết

a)  Ta có:\(C = A + B\)\(\begin{array}{l} = \left( {{x^2} - 3xy + 2{y^2}} \right) + \left( {{y^2} + 2xy + {x^2} + 1} \right)\\ = {x^2} - 3xy + 2{y^2} + {y^2} + 2xy + {x^2} + 1\\ = \left( {{x^2} + {x^2}} \right) + \left( { - 3xy + 2xy} \right) + \left( {2{y^2} + {y^2}} \right) + 1\\ = 2{x^2} - xy + 3{y^2} + 1\end{array}\)Vậy \(C = 2{x^2} - xy + 3{y^2} + 1\)b) Ta có: \(D + A = B \Rightarrow D = B - A\)\(\begin{array}{l}D = \left( {{y^2} + 2xy + {x^2} + 1} \right) - \left( {{x^2} - 3xy + 2{y^2}} \right)\\ = {y^2} + 2xy + {x^2} + 1 - {x^2} + 3xy - 2{y^2}\\ = \left( {{x^2} - {x^2}} \right) + \left( {3xy + 2xy} \right) + \left( { - 2{y^2} + {y^2}} \right) + 1\\ =  - {y^2} + 5xy + 1\end{array}\)Vậy \(D =  - {y^2} + 5xy + 1\)

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