Cho các đa thức
\(\eqalign{ & P\left( x \right) = 3{x^2} - 4x + 1 \cr & Q\left( x \right) = 5{x^3} - 2x - 4 \cr & R\left( x \right) = 2x - 7{x^4} + 3 \cr}\)
Hãy tính P(x) + Q(x) + R(x) và
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P(x) - Q(x) - R(x).
\(\eqalign{ & P(x) + Q(x) + R(x) = (3{x^2} - 4x + 1) + (5{x^3} - 2x - 4) + (2x - 7{x^4} + 3) \cr & = 3{x^2} - 4x + 1 + 5{x^3} - 2x - 4 + 2x - 7{x^4} + 3 \cr & = 3{x^2} + ( - 4x - 2x + 2x) + (1 - 4 + 3) + 5{x^3} - 7{x^4} = 3{x^2} - 4x + 5{x^3} - 7{x^4}. \cr & P(x) - Q(x) - R(x) = (3{x^2} - 4x + 1) - (5{x^3} - 2x - 4) - (2x - 7{x^4} + 3) \cr & = 3{x^2} - 4x + 1 - 5{x^3} + 2x + 4 - 2x + 7{x^4} - 3 \cr & = 3{x^2} + ( - 4x + 2x - 2x) + (1 + 4 - 3) - 5{x^3} + 7{x^4} = 3{x^2} - 4x + 2 - 5{x^3} + 7{x^4}. \cr}\)