Expand (Algebra) — Definition, Formula & Examples
Expanding is the process of multiplying out parentheses in an algebraic expression so that no grouped terms remain. You rewrite a product like as a sum .
To expand an algebraic expression is to apply the distributive property of multiplication over addition (and subtraction) repeatedly until the expression is written as a polynomial in standard form — a sum of individual terms with no remaining parenthesized factors.
Key Formula
Where:
- = The factor being distributed
- = Terms inside the parentheses
How It Works
Start by identifying the factor outside the parentheses and each term inside. Multiply the outside factor by every inside term, keeping correct signs. When two binomials are multiplied, such as , distribute each term of the first binomial across the second, producing four products. After multiplying, combine any like terms to simplify the result.
Worked Example
Problem: Expand .
Distribute the first term: Multiply by each term in the second binomial.
Distribute the second term: Multiply by each term in the second binomial.
Combine like terms: Add the four products together and simplify.
Answer:
Why It Matters
Expanding is the reverse of factoring, and you need both skills to solve quadratic equations and simplify rational expressions. In physics and engineering, expanding products of polynomials is a routine step when modeling area, force, or growth.
Common Mistakes
Mistake: Forgetting to distribute the sign: writing as instead of .
Correction: Treat as a single signed number. When you multiply by , the product is , not .