Cho hàm số y = f(x) = ax^2 + bx + c. Rút gọn biểu thức

* Hướng dẫn giải

Đáp án D

Ta có: 

f(x+ 3) - 3f(x + 2) + 3f(x + 1)

 = a(x +3)${}^2$+ b (x +3) + c - 3a. (x+ 2)${}^2$- 3b.(x + 2) - 3x 

      + 3. a(x+1)${}^2$+ 3b(x +1) + 3c

$$\begin{gathered} = a(x^2 +\hspace{0.17em}6x + 9) +\hspace{0.17em}bx+ 3b +\hspace{0.17em}c - 3a(x^2+ 4x + 4)- 3bx- 6b- 3c \\ +\hspace{0.17em}3a(x^2+ 2x + 1) +\hspace{0.17em}3bx+ 3b+ 3c \\ = x^2(a - 3a+\hspace{0.17em}3a)\hspace{0.17em}+\hspace{0.17em}x. (6a +\hspace{0.17em}b - 12a- 3b+\hspace{0.17em}6a+\hspace{0.17em}3b) \\ +\hspace{0.17em}(9a\hspace{0.17em}+ 3b + c- 12a- 6b- 3c+\hspace{0.17em}3a+\hspace{0.17em}3b +\hspace{0.17em}3c) \\ = a{x}^2+\hspace{0.17em}bx+\hspace{0.17em}c \end{gathered}$$