Algebraic Expression Simplifier - Simplify, Expand, Factor | 8gwifi.org

Algebraic Expression Simplifier

Simplify, expand, and factor algebraic expressions with step-by-step solutions

Enter Expression
Use ^ for exponents, * for multiplication, / for division
Simplify:
Combines like terms and reduces to simplest form
Expand:
Multiplies out brackets and parentheses
Factor:
Factors the expression into products
Show all:
Performs all operations: simplify, expand, and factor
Examples:
• (x + 2)(x + 3) → Expand
• x^2 + 5*x + 6 → Factor
• 2*x + 3*x - x → Simplify
• (a + b)^2 → Expand
• x^2 - 9 → Factor
Simplification Rules
Combining Like Terms

Terms with the same variables and exponents can be combined:

3x + 5x = 8x
2x² + 7x² = 9x²
4xy - 2xy = 2xy

Note: 3x + 5x² cannot be combined (different exponents)

Expanding Expressions

Distributive Property:

a(b + c) = ab + ac
3(x + 2) = 3x + 6

FOIL Method (First, Outer, Inner, Last):

(a + b)(c + d) = ac + ad + bc + bd
(x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6

Special Products:

  • Square of sum: (a + b)² = a² + 2ab + b²
  • Square of difference: (a - b)² = a² - 2ab + b²
  • Difference of squares: (a + b)(a - b) = a² - b²
Factoring

Greatest Common Factor (GCF):

6x + 9 = 3(2x + 3)
4x² + 8x = 4x(x + 2)

Difference of Squares:

a² - b² = (a + b)(a - b)
x² - 9 = (x + 3)(x - 3)

Perfect Square Trinomials:

x² + 6x + 9 = (x + 3)²
x² - 10x + 25 = (x - 5)²
Simplifying Fractions
(6x² + 9x) / 3x = (3x(2x + 3)) / 3x = 2x + 3
Order of Operations

PEMDAS/BODMAS:

  1. Parentheses/Brackets
  2. Exponents/Orders
  3. Multiplication & Division (left to right)
  4. Addition & Subtraction (left to right)
Simplification Strategy
  1. Remove parentheses (expand if needed)
  2. Combine like terms
  3. Factor out GCF if possible
  4. Look for special patterns (difference of squares, etc.)
  5. Cancel common factors in fractions
Result

Enter an expression and select an operation to see the result

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