Last Updated: November 21, 2025
Basic Operations
| Rule | Formula |
|---|---|
Addition
|
a + b = b + a |
Multiplication
|
a × b = b × a |
Distributive
|
a(b + c) = ab + ac |
Power of a product
|
(ab)ⁿ = aⁿbⁿ |
Power of a power
|
(aⁿ)ᵐ = aⁿᵐ |
Solving Equations
Linear: ax + b = c
Isolate x: x = (c - b) / a
Quadratic: ax² + bx + c = 0
Use formula: x = (-b ± √(b² - 4ac)) / 2a
Square both sides
Solve equations with square roots
Factoring
| Pattern | Factored Form |
|---|---|
x² - y²
|
(x + y)(x - y) |
x² + 2xy + y²
|
(x + y)² |
x² - 2xy + y²
|
(x - y)² |
💡 Pro Tip:
Always check your answer by substituting back into the original equation!