Chapter 1 - Introduction to Algebraic Expressions - 1.8 Exponential Notation and Order of Operations - 1.8 Exercise Set - Page 67: 115

The square of negative $x$ is not equal to the negative of the square of $x$. We know that $(-x)^2=(-x)\cdot(-x)$. Since the product of even number of the negative numbers is positive. We get, $(-x)^2=x^2$ Hence, $(-x)^2$ is not equivalent to $-x^2$.

The square of negative $x$ is not equal to the negative of the square of $x$. We know that $(-x)^2=(-x)\cdot(-x)$. Since the product of even number of the negative numbers is positive. We get, $(-x)^2=x^2$ Hence, $(-x)^2$ is not equivalent to $-x^2$.