1. Stating the problem: We need to expand and simplify the expressions for A, B, C, D, E, and F. 2. Recall the formulas: - Square of a binomial: $ (a+b)^2 = a^2 + 2ab + b^2 $ - Difference of squares: $ (a-b)(a+b) = a^2 - b^2 $ 3. Expand each expression: A: $ (x+10)^2 = x^2 + 2 \cdot x \cdot 10 + 10^2 = x^2 + 20x + 100 $ B: $ (5 - x)^2 = (-(x - 5))^2 = (x - 5)^2 = x^2 - 2 \cdot x \cdot 5 + 5^2 = x^2 - 10x + 25 $ C: $ (y - 8)(y + 8) = y^2 - 8^2 = y^2 - 64 $ D: $ (2x - 1)^2 = (2x)^2 - 2 \cdot 2x \cdot 1 + 1^2 = 4x^2 - 4x + 1 $ E: $ (3x + 4)^2 = (3x)^2 + 2 \cdot 3x \cdot 4 + 4^2 = 9x^2 + 24x + 16 $ F: $ (5y + 2)(9y - 2) = 5y \cdot 9y + 5y \cdot (-2) + 2 \cdot 9y + 2 \cdot (-2) = 45y^2 - 10y + 18y - 4 = 45y^2 + 8y - 4 $ Final answers: A = $x^2 + 20x + 100$ B = $x^2 - 10x + 25$ C = $y^2 - 64$ D = $4x^2 - 4x + 1$ E = $9x^2 + 24x + 16$ F = $45y^2 + 8y - 4$