1. The problem provides columns labeled $x$, $y$, $xy$, $x^2$, and $y^2$ with numerical data. 2. The columns $xy$, $x^2$, and $y^2$ represent derived values from $x$ and $y$: - $xy$ is the product of $x$ and $y$, calculated as $xy = x \times y$. - $x^2$ is the square of $x$, calculated as $x^2 = x \times x$. - $y^2$ is the square of $y$, calculated as $y^2 = y \times y$. 3. To verify or compute these values for any given $x$ and $y$, use the formulas above. 4. For example, if $x=54$ and $y=15$: - $xy = 54 \times 15 = 810$ - $x^2 = 54^2 = 2916$ - $y^2 = 15^2 = 225$ 5. This matches the provided data, confirming the relationships. 6. Therefore, the equalities are: $$xy = x \times y$$ $$x^2 = x \times x$$ $$y^2 = y \times y$$ 7. These formulas allow you to compute the columns $xy$, $x^2$, and $y^2$ from $x$ and $y$ values.