Bài 1: Cho \(A = 2{{\rm{a}}^2} – 3{\rm{a}}b + 4{b^2};\)\(\;B = 3{{\rm{a}}^2} + 4{\rm{a}}b – {b^2};\)\(\;C = {a^2} + 2{\rm{a}}b + 3{b^2}.\) Tìm \(A – B + C\).
Bài 2: Thu gọn đa thức:
\(M = 3{{\rm{x}}^2} + 5{\rm{x}}y + 7{{\rm{x}}^2}y – {\rm{[}}(5{\rm{x}}y + 3{{\rm{x}}^2}) – (7{{\rm{x}}^2}y – 3{x^2}){\rm{]}}.\)
Bài 3: Tìm đa thức P, biết:
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\(P – (3{\rm{x}}y – 3{{\rm{x}}^3}y + x{y^3} – {x^2}{y^2}) = 2{{\rm{x}}^2}{y^2} + 2{x^3}y – xy + x{y^3}.\)
Bài 1: Ta có:
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\(\eqalign{ A – B + C &= (2{{\rm{a}}^2} – 3{\rm{a}}b + 4{b^2}) – (3{{\rm{a}}^2} + 4{\rm{a}}b – {b^2}) + ({a^2} + 2{\rm{a}}b + 3{b^2}) \cr & {\rm{ }} = 2{{\rm{a}}^2} – 3{\rm{a}}b + 4{b^2} – 3{{\rm{a}}^2} – 4{\rm{a}}b + {b^2} + {a^2} + 2{\rm{a}}b + 3{b^2} \cr & {\rm{ }} = – 5{\rm{a}}b + 8{b^2}. \cr} \)
Bài 2: Ta có:
\(\eqalign{ M &= 3{{\rm{x}}^2} + 5{\rm{x}}y + 7{{\rm{x}}^2}y – (5{\rm{x}}y + 3{{\rm{x}}^2} – 7{{\rm{x}}^2}y + 3{x^2}) \cr & {\rm{ }} = {{\rm{x}}^2} + 5{\rm{x}}y + 7{{\rm{x}}^2}y – 5{\rm{x}}y – 3{{\rm{x}}^2} + 7{{\rm{x}}^2}y – 3{x^2} \cr & {\rm{ }} = – 3{{\rm{x}}^2} + 14{{\rm{x}}^2}y. \cr} \)
Bài 3: Ta có:
\(P = 2{{\rm{x}}^2}{y^2} + 2{x^3}y – xy + x{y^3} + 3{\rm{x}}y – 3{{\rm{x}}^3}y + x{y^3} – {x^2}{y^2} \)
\(\;\;\;\;= {x^2}{y^2} – {x^3}y + 2{\rm{x}}y + 2x{y^3}.\)
