1. **State the problem:** We need to expand and simplify the expression $$(7-5y)^2$$. 2. **Formula used:** The square of a binomial $(a-b)^2$ is given by the formula: $$ (a-b)^2 = a^2 - 2ab + b^2 $$ This means we square the first term, subtract twice the product of the two terms, and then add the square of the second term. 3. **Apply the formula:** Here, $a=7$ and $b=5y$. $$ (7-5y)^2 = 7^2 - 2 \times 7 \times 5y + (5y)^2 $$ 4. **Calculate each term:** $$ 7^2 = 49 $$ $$ -2 \times 7 \times 5y = -70y $$ $$ (5y)^2 = 25y^2 $$ 5. **Combine all terms:** $$ 49 - 70y + 25y^2 $$ 6. **Final answer:** The expanded form of $$(7-5y)^2$$ is: $$ 25y^2 - 70y + 49 $$ This is the simplified polynomial after expanding the square of the binomial.