Expand (a+b)(a-b)

Expand and distribute algebraic expressions using FOIL and distribution.

Expression

Answer

a^2 − b^2

To expand (a+b)(a-b), use the FOIL method — multiply each term in the first binomial by each term in the second, then combine like terms.

(a+b)(a-b)

Step 1 — Multiply each term in the first by each term in the second

a · a = a²

a · -b = -ab

b · a = ab

b · -b = -b²

Step 2 — Combine like terms

= a² − b²

a² − b²

How to expand (a+b)(a-b)

To expand (a+b)(a-b), distribute each term across the other factor and combine like terms. The result is a^2 − b^2.

This is a algebraic expansion — we multiply out brackets and simplify. For binomials, the FOIL method (First, Outer, Inner, Last) is commonly used.

Frequently asked questions

What is the answer to (a+b)(a-b)?
The answer is a^2 − b^2.

What method is used?
the distributive property (FOIL for two binomials) — multiply each term in one factor by every term in the other, then combine like terms.