Question

Chứng minh đẳng thức:

\(x\left(x+1\right)\left(x+2\right)=x^3+3\text{x}^2+2\text{x}\)

Answer 1

Ta có:\(x\left(x+1\right)\left(x+2\right)=\left(x^2+x\right)\left(x+2\right)=x^3+2x^2+x^2+2x=x^3+3x^2+2x\)

Vậy....

Answer 2

ta có : \(VP=x^3+3x^2+2x=x\left(x^2+3x+2\right)=x\left(x^2+x+2x+2\right)\)

\(=x\left(x\left(x+1\right)+2\left(x+1\right)\right)=x\left(x+2\right)\left(x+1\right)=VT\)

vậy \(x\left(x+1\right)\left(x+2\right)=x^3+3x^2+2x\) (đpcm)

Answer 3

Ta có \(VT\) :

\(x\left(x+1\right)\left(x+2\right)=x^3+2x^2+x^2+2x=x^3+3x^2+2x=VP\)

\(\Rightarrowđpcm\)