Question

\(y=f\left(x\right)=ax^2+bx+c\) .Biểu thức f(x+3)-3f(x+2)+3f(x+1). Có giá trị bằng ?

Answer 1

\(f\left(x+3\right)-3f\left(x+2\right)+3f\left(x+1\right)\)

\(=a\left(x+3\right)^2+b\left(x+3\right)+c-3\left[a\left(x+2\right)^2+b\left(x+2\right)+c\right]+3\left[a\left(x+1\right)^2+b\left(x+1\right)+c\right]\)

\(=3a\left(x+1\right)^2+a\left(x+3\right)^2-3a\left(x+2\right)^2+bx+c\)

\(=ax^2+bx+c\)