Distributive Property

The distributive property states that the multiplication "distributes" over addition. Thus a × (b + c) = a × b + a × c and (b + c) × a = b × a + c × a for all real or complex numbers a, b, and c.

The distributive property is behind the common multiplication algorithm. For example, 27 × 4 means 4 × (2 tens + 7 ones). To complete the multiplication, you use the distributive property: 4 × (20 + 7) = (4 × 20) + (4 × 7) = 80 + 28 = 108.

We use the distributive property more than once in carrying out such computations as (3x + 4)(x + 2). Thus (3x + 4)(x + 2) = (3x + 4)x + (3x + 4)2 where 3x + 4 is "distributed over" x + 2 and then (3x + 4)x + (3x + 4)2 = 3x² + 4x) + (6x + 8) = 3x² + 10x + 8 where x and 2 are "distributed" over 3x + 4.