Final answer:
To show the equivalence between the expressions, we can expand and simplify the equation step by step.
Step-by-step explanation:
To show that -x^2-10x-15 is equivalent to -(x+5)^2+10, we can expand the square on the right hand side and simplify the equation. Let's start by expanding (x+5)^2, which gives us x^2+10x+25. Then, when we multiply by -1, we get -x^2-10x-25. Finally, if we add 10 to this expression, we get -x^2-10x-15, which is equivalent to the expression on the left side.