Factor the expression completely.
−9x ^3+72x ^5
To factor the expression completely, we can start by finding the common factor of the terms. In this case, the common factor is -9x^3. Factoring it out, we have:
-9x^3 + 72x^5 = -9x^3(1 - 8x^2)
Now, we can further factor the expression inside the parentheses. It is a difference of squares, so we can rewrite it as:
1 - 8x^2 = (1 - √8x)(1 + √8x)
Therefore, the completely factored expression is:
-9x^3(1 - √8x)(1 + √8x)