FOIL: Multiply Two Binomials Step by Step

FOIL is a handy way to multiply two binomials. The letters stand for First, Outer, Inner, and Last: multiply those four pairs, then add the results and combine like terms.

Worked example: (x + 3)(x + 2)

Multiply (x + 3)(x + 2) step by step.

• First: x times x = x²
• Outer: x times 2 = 2x
• Inner: 3 times x = 3x
• Last: 3 times 2 = 6

Add the four products: x² + 2x + 3x + 6. Combine the like terms 2x and 3x to get 5x.

Answer: (x + 3)(x + 2) = x² + 5x + 6

Check your own FOIL work with a foil calculator.

Practice problem

Multiply (x + 4)(x + 1) using FOIL. Work out the First, Outer, Inner, and Last products, add them, and combine like terms. (Answer: x² + 5x + 4.)