1. **State the problem:** We have a table with two expressions: $x^2 + y$ and $xy$, and some values to find. 2. **Given values:** - For $x=3$, $y=5$, $x^2 + y = 14$, and $xy = A$ (unknown). - For $x=4$, $y=B$ (unknown), $x^2 + y = C$ (unknown), and $xy = 8$. 3. **Find $A$ when $x=3$, $y=5$:** Use the formula for $xy$: $$xy = 3 \times 5 = 15$$ So, $A = 15$. 4. **Find $B$ when $x=4$, $xy=8$:** Use the formula for $xy$: $$xy = 8 \implies 4 \times y = 8$$ Divide both sides by 4: $$\cancel{4} \times y = \frac{8}{\cancel{4}} \implies y = 2$$ So, $B = 2$. 5. **Find $C$ when $x=4$, $y=2$:** Use the formula for $x^2 + y$: $$x^2 + y = 4^2 + 2 = 16 + 2 = 18$$ So, $C = 18$. **Final answers:** - $A = 15$ - $B = 2$ - $C = 18$