Cho hàm số \(f\left(x\right)=ax^2+bx+c\). Rút gọn biểu thức \(f\left(x+3\right)-3f\left(x+2\right)+3f\left(x+1\right)\) \(ax^2-bx-c\) \(ax^2+bx-c\) \(ax^2-bx+c\) \(ax^2+bx+c\) Hướng dẫn giải: \(f\left(x+3\right)=a\left(x+3\right)^2+b\left(x+3\right)+c=ax^2+\left(6a+b\right)x+\left(9a+3b+c\right)\) \(f\left(x+2\right)=a\left(x+2\right)^2+b\left(x+2\right)+c=ax^2+\left(4a+b\right)x+\left(4a+2b+c\right)\) \(f\left(x+1\right)=a\left(x+1\right)^2+b\left(x+1\right)+c=ax^2+\left(2a+b\right)x+\left(a+b+c\right)\) Biểu thức cần rút gọn là \(ax^2+\left(6a+b\right)x+\left(9a+3b+c\right)-3\left[ax^2+\left(4a+b\right)x+\left(4a+2b+c\right)\right]\)\(+3\left(ax^2+\left(2a+b\right)x+\left(a+b+c\right)\right)\) \(=ax^2+bx+c\)
