(3x+1)(x-2)(x+3)-(x-2)(2x+1)(x-4)

asked by guest
on Jan 29, 2025 at 7:20 pm



You asked:

Evaluate the expression: (3x+1)(x2)(x+3)(x2)(2x+1)(x4)\left(3 x + 1\right) \left(x - 2\right) \left(x + 3\right) - \left(x - 2\right) \left(2 x + 1\right) \left(x - 4\right)

MathBot Answer:

Evaluated



(3x+1)(x2)(x+3)(x2)(2x+1)(x4)=(2x+1)(x4)(x2)+(3x+1)(x2)(x+3)\displaystyle \left(3 x + 1\right) \left(x - 2\right) \left(x + 3\right) - \left(x - 2\right) \left(2 x + 1\right) \left(x - 4\right) = - \left(2 x + 1\right) \left(x - 4\right) \left(x - 2\right) + \left(3 x + 1\right) \left(x - 2\right) \left(x + 3\right)


Expanded

(3x+1)(x2)(x+3)(x2)(2x+1)(x4)=x3+15x227x14\left(3 x + 1\right) \left(x - 2\right) \left(x + 3\right) - \left(x - 2\right) \left(2 x + 1\right) \left(x - 4\right) = x^{3} + 15 x^{2} - 27 x - 14


Factored

(3x+1)(x2)(x+3)(x2)(2x+1)(x4)=(x2)(x2+17x+7)\left(3 x + 1\right) \left(x - 2\right) \left(x + 3\right) - \left(x - 2\right) \left(2 x + 1\right) \left(x - 4\right) = \left(x - 2\right) \left(x^{2} + 17 x + 7\right)