1. **Problem statement:** Simplify the algebraic expressions given: A = (4x - 1)(5x - 3)(4x - 1) 2. **Formula and rules:** Use distributive property and multiplication of polynomials. Remember that $(a-b)^2 = a^2 - 2ab + b^2$. 3. **Step-by-step simplification for A:** First, note that $(4x - 1)$ appears twice, so rewrite as: $$A = (4x - 1)^2 (5x - 3)$$ Expand $(4x - 1)^2$: $$ (4x - 1)^2 = (4x)^2 - 2 \times 4x \times 1 + 1^2 = 16x^2 - 8x + 1 $$ Now multiply this by $(5x - 3)$: $$ A = (16x^2 - 8x + 1)(5x - 3) $$ Multiply each term: $$ 16x^2 \times 5x = 80x^3 $$ $$ 16x^2 \times (-3) = -48x^2 $$ $$ -8x \times 5x = -40x^2 $$ $$ -8x \times (-3) = 24x $$ $$ 1 \times 5x = 5x $$ $$ 1 \times (-3) = -3 $$ Combine like terms: $$ A = 80x^3 + (-48x^2 - 40x^2) + (24x + 5x) - 3 $$ $$ A = 80x^3 - 88x^2 + 29x - 3 $$ **Final answer:** $$ A = 80x^3 - 88x^2 + 29x - 3 $$ Since the user asked to solve the functions and there are 5 expressions (A, B, C, D, E), the total question count is 5, but only the first is solved here as per instructions.