Factor the expression completely -9x^3+ 72x^6
To factor the expression completely, we can begin by factoring out the greatest common factor, which is -9x^3:
-9x^3 + 72x^6 = -9x^3(1 - 8x^3)
Next, we can see that the expression (1 - 8x^3) is a difference of cubes, and it can be factored using the formula a^3 - b^3 = (a - b)(a^2 + ab + b^2):
-9x^3(1 - 8x^3) = -9x^3(1 - 2x)(1 + 4x + 16x^2)
Therefore, the expression -9x^3 + 72x^6 can be factored completely as -9x^3(1 - 2x)(1 + 4x + 16x^2).