1. **State the problem:** Simplify the expression $$A = (5x+3)^2 - (5x-3)(2x+1)$$. 2. **Use formulas:** Recall the formulas for expansion: - Square of a binomial: $$(a+b)^2 = a^2 + 2ab + b^2$$ - Product of binomials: $$(a-b)(c+d) = ac + ad - bc - bd$$ 3. **Expand each term:** - Expand $$(5x+3)^2$$: $$ (5x)^2 + 2 \cdot 5x \cdot 3 + 3^2 = 25x^2 + 30x + 9 $$ - Expand $$(5x-3)(2x+1)$$: $$ 5x \cdot 2x + 5x \cdot 1 - 3 \cdot 2x - 3 \cdot 1 = 10x^2 + 5x - 6x - 3 = 10x^2 - x - 3 $$ 4. **Substitute expansions back into A:** $$ A = (25x^2 + 30x + 9) - (10x^2 - x - 3) $$ 5. **Distribute the minus sign:** $$ A = 25x^2 + 30x + 9 - 10x^2 + x + 3 $$ 6. **Combine like terms:** $$ A = (25x^2 - 10x^2) + (30x + x) + (9 + 3) = 15x^2 + 31x + 12 $$ **Final answer:** $$\boxed{15x^2 + 31x + 12}$$