Simplifying
(1 + x)(3 + 2x)

Multiply (1 + x) * (3 + 2x)
(1(3 + 2x) + x(3 + 2x))
((3 * 1 + 2x * 1) + x(3 + 2x))
((3 + 2x) + x(3 + 2x))
(3 + 2x + (3 * x + 2x * x))
(3 + 2x + (3x + 2x2))

Combine like terms: 2x + 3x = 5x
(3 + 5x + 2x2)