Multiply the 2 binomials using FOIL:
(2x + 1)(4x + 1)
First-Outside-Inside-Last:
(a + b)(c + d) = (a * c) + (b * c) + (a * d) + (b * d)
a = 2x, b = 1, c = 4x, and d = 1
(2x + 1)(4x + 1) = (2x * 4x) + (1 * 4x) + (2x * 1) + (1 * 1)
(2x + 1)(4x + 1) = 8x2 + 4x + 2x + 1