Expand & Simplify

Expression Setup

Expression

Supports: a(bx+c), (ax+b)(cx+d), (ax+b)², (ax+b)³

Examples

Polynomial Expression

Enter a polynomial with like terms to combine. Supports x², x³, constant terms.

Examples

First Polynomial

Second Polynomial

Each polynomial is multiplied term-by-term. Works for any degree.

Examples

Result

Enter an expression above and press Expand & Simplify to see the expanded form, step-by-step work, and a term breakdown.

Simplified Form

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Terms After Simplifying

FOIL Method

(ax+b)(cx+d) = F + O + I + L

F — First: Multiply the first terms of each binomial: ax · cx = acx²

O — Outer: Multiply the outer terms: ax · d = adx

I — Inner: Multiply the inner terms: b · cx = bcx

L — Last: Multiply the last terms: b · d = bd

Then combine the two x terms (O + I) to get the middle coefficient.

Distribution is the general rule: a(b+c) = ab+ac. FOIL is just distribution applied twice — once for each term in the first binomial.

Common Patterns

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

These patterns let you skip FOIL for special products. Recognize them by looking at whether both binomials are the same or differ only by sign.

(a+b)³ expands to a³ + 3a²b + 3ab² + b³ (Pascal's row 3).