The Distributive Law

1. F (First): the product of the first terms
   x·x = x·x
2. O (Outer): the product of the outer terms
   x·2 = x·2
3. I (Inner): the product of the inner terms
   1·x = x
4. L (Last): the product of the last terms
   1·2 = 2
5. Add all four terms together
   x·x + x·2 + x + 2

The distributive law: a(b+c) = ab + ac. Why does it work? When you multiply a number by a sum, the multiplication distributes over each term. You can see this visually: a rectangle with height a and width b+c has the same area as the two rectangles a·b + a·c added together.

FOIL is a memory aid — First, Outer, Inner, Last — for the four products you need when expanding brackets in (a+b)(c+d): ac, ad, bc, bd.

The standard identities:

• (a+b)² = a² + 2ab + b²
• (a−b)² = a² − 2ab + b²
• (a+b)(a−b) = a² − b²

Worked examples:

• 3(x+5) = 3x + 15
• (x+2)(x+3) = x² + 5x + 6
• (x+4)² = x² + 8x + 16

Common mistake: (a+b)² ≠ a²+b²! You must remember the middle term 2ab. For example (3+4)² = 49, not 9+16 = 25.

💼 The distributive law is used throughout mathematics, physics (kinematics and motion), economics (interest calculations) and any field involving algebraic equations.