1. **State the problem:** Simplify the expression $3y \times 5y$. 2. **Recall the multiplication rule for variables:** When multiplying terms with the same base, multiply the coefficients and add the exponents of the variables. 3. **Apply the rule:** $$3y \times 5y = (3 \times 5)(y \times y) = 15y^{1+1} = 15y^2$$ 4. **Final answer:** The simplified expression is $15y^2$. This means you multiply the numbers 3 and 5 to get 15, and since $y$ is multiplied by itself, you add the exponents (1 + 1) to get $y^2$.