What is the product of -2x^3 + x - 5 and x^3 - 3x - 4 ? Show your work. Is the product of x^3 - 3x - 4 and -2x^3 + x - 5 equal to the product of and ? Explain your answer.

For this case we must find the product of the following expressions:[tex](-2x ^ 3 + x-5) (x ^ 3-3x-4)[/tex]We apply distributive property, that is, we multiply term by term, taking into account that:[tex]- * - = +\\- * + = -[/tex][tex]-2x ^ {3 + 3} + 6x^{3 + 1} + 8x ^ 3 + x ^ {1 + 3} -3x1 + 1 -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 6 + 6x ^ 4 + 8x ^ 3 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]If we multiply:[tex](x ^ 3-3x-4) (- 2x ^ 3 + x-5)[/tex]We will obtain the same result because we would be applying the commutative property of multiplication.ANswer:[tex]-2x ^ 6 + 6x ^ 4 + 8x ^ 3 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20[/tex]