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Phép cộng, phép trừ đa thức

Cộng và trừ hai đa thức như thế nào?
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1. Lý thuyết

- Khái niệm:

Cộng (hay trừ) hai đa thức🌞 tức là thu gọn đa thức nhận được sau khi nối hai đa thức đã cho bởi dấu “+” (hay dấu “–”)

- Tính chất phép cộng đa thức:

+ Giao hoán: A + B = B + A

+ Kết hợp: (A + B) + C = A + (B + C)

- Quy tắc cộng, trừ hai đa thức: Để cộng, trừ hai đa thức ta thực hiện các bước:

+ Bỏ dấu ngoặc (sử dụng quy tắc dấu ngoặc);+ Nhóm các đơn thức đồng dạng (sử dụng tính chất giao hoán và kết hợp);+ Cộng, trừ các đơn thức đồng dạng.

2. Ví dụ minh họa

Cho hai đa thức \(A = 3{x^2} - xy\)và \(B = {x^2} + 2xy - {y^2}\)\(\begin{array}{l}A + B = \left( {3{x^2} - xy} \right) + \left( {{x^2} + 2xy - {y^2}} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\, = 3{x^2} - xy + {x^2} + 2xy - {y^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\, = (3{x^2} + {x^2}) + ( - xy + 2xy) - {y^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\, = 4{x^2} + xy - {y^2}\end{array}\)\(\begin{array}{l}A - B = \left( {3{x^2} - xy} \right) - \left( {{x^2} + 2xy - {y^2}} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\, = 3{x^2} - xy - {x^2} - 2xy + {y^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\, = (3{x^2} - {x^2}) + ( - xy - 2xy) + {y^2}\\\,\,\,\,\,\,\,\,\,\,\,\,\, = 2{x^2} - 3xy + {y^2}\end{array}\)

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