Bài 7.18 trang 28 SBT Toán lớp 7 Kết nối tri thức: Cho các đa thức (Aleft( x right) = 2{x^3} - 2{x^2} + x - 4;Bleft( x right) = 3{...

Cho các đa thức $A\left( x \right) = 2{x^3} - 2{x^2} + x - 4;B\left( x \right) = 3{x^3} - 2x + 3;C\left( x \right) =  - {x^3} + 1$. Hãy tính:

a)$A\left( x \right) + B\left( x \right) + C\left( x \right);$

b) $A\left( x \right) - B\left( x \right) - C\left( x \right).$ 

$\begin{array}{l}A + B + C = A + \left( {B + C} \right)\\A - B - C = A - \left( {B + C} \right)\end{array}$

Tính B + C

a)

$\begin{array}{l}A\left( x \right) + B\left( x \right) + C\left( x \right)\\ = A\left( x \right) + \left[ {B\left( x \right) + C\left( x \right)} \right]\\ = 2{x^3} - 2{x^2} + x - 4 + \left( {3{x^3} - 2x + 3 - {x^3} + 1} \right)\\ = 2{x^3} - 2{x^2} + x - 4 + 2{x^3} - 2x + 4\\ = \left( {2{x^3} + 2{x^3}} \right) - 2{x^2} + \left( {x - 2x} \right) + \left( { - 4 + 4} \right)\\ = 4{x^3} - 2{x^2} - x\end{array}$

b)

$\begin{array}{l}A\left( x \right) - B\left( x \right) - C\left( x \right)\\ = A\left( x \right) - \left[ {B\left( x \right) + C\left( x \right)} \right]\\ = 2{x^3} - 2{x^2} + x - 4 - \left( {3{x^3} - 2x + 3 - {x^3} + 1} \right)\\ = 2{x^3} - 2{x^2} + x - 4 - 2{x^3} + 2x - 4\\ = \left( {2{x^3} - 2{x^3}} \right) - 2{x^2} + \left( {x + 2x} \right) + \left( { - 4 - 4} \right)\\ =  - 2{x^2} + 3x - 8\end{array}$