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
\(ax^2+\left(6a+b\right)x+\left(9a+3b+c\right)-3\left[ax^2+\left(4a+b\right)x+\left(4a+2b+c\right)\right]\)\(+3\left(ax^2+\left(2a+b\right)x+\left(a+b+c\right)\right)\)
\(=ax^2+bx+c\)