Find each product. 17) (4m-3)(8m+1) 19) (5n-4)(4n^2+4n-1) 18) (7x+5)(4x-4) 20) (n-6)(n^2+7n+4)

17) To find the product of , we can use the distributive property (also known as the FOIL method for binomials). First, multiply the first terms: .Next, multiply the outer terms: .Then, multiply the inner terms-3 \cdot 8m = -24m -3 \cdot 1 = -3 32m^2 + 4m - 24m - 3 = 32m^2 - 20m - 3 (4m-3)(8m+1) 32m^2 - 20m - 3 (5n-4)(4n^2+4n-1) 5n \cdot 4n^2 = 20n^3 5n \cdot 4n = 20n^2 5n \cdot (-1) = -5n -4 \cdot 4n^2 = -16n^2 -4 \cdot 4n = -16n -4 \cdot (-1) = 4 20n^3 + 20n^2 - 5n - 16n^2 - 16n + 4 = 20n^3 + 4n^2 - 21n + 4 (5n-4)(4n^2+4n-1) 20n^3 + 4n^2 - 21n + 4 (7x+5)(4x-4) 7x \cdot 4x = 28x^2 7x \cdot (-4) = -28x 5 \cdot 4x = 20x 5 \cdot (-4) = -20 28x^2 - 28x + 20x - 20 = 28x^2 - 8x - 20 (7x+5)(4x-4) 28x^2 - 8x - 20 (n-6)(n^2+7n+4) n \cdot n^2 = n^3 n \cdot 7n = 7n^2 n \cdot 4 = 4n -6 \cdot n^2 = -6n^2 -6 \cdot 7n = -42n -6 \cdot 4 = -24 n^3 + 7n^2 + 4n - 6n^2 - 42n - 24 = n^3 + n^2 - 38n - 24 (n-6)(n^2+7n+4) n^3 + n^2 - 38n - 24$.