Question

Rút gọn biểu thức.

a) (x+2)³-(x+1)³

b) (x-3)³-x(x-3)²

c) (x+1)³-x²(x+1)-2x(x+2)

Answer 1

a: =x^3+6x^2+12x+8-(x^3+3x^2+3x+1)

=x^3+6x^2+12x+8-x^3-3x^2-3x-1

=3x^2+9x+7

b: =x^3-9x^2+27x-27-x(x^2-6x+9)

=x^3-9x^2+27x-27-x^3+6x^2-9x

=-3x^2+18x-27

c: =x^3+3x^2+3x+1-x^3-x^2-2x^2-4x

=-x+1

Answer 2

\(a,\left(x+2\right)^3-\left(x+1\right)^3\\ =\left(x+2-x-1\right)\left(x^2+4x+4+x^2+3x+2+x^2+2x+1\right)\\ =3x^2+9x+7\\ b,\left(x-3\right)^3-x\left(x-3\right)^2\\ =x^3-6x^2+9x-27-x^3+6x^2-9x\\ =-27\)