# Basic Rules of Algebra

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Property | Example | Definition | Term |
---|---|---|---|

a + b = b + a | 4x + x^2 = x^2 + 4x | Use this rule when adding two real numbers, variables, or algebraic expressions | Commutative Property of Addition |

ab = ba | (1 - x)x^2 = x^2(1 - x) | Use this rule when multiplying two real numbers, variables, or algebraic expressions | Commutative Property of Multiplication |

(a + b) + c = a + (b + c) | (x + 5) + x^2 = x + (5 + x^2) | Use this rule when adding three real numbers, variables, or algebraic expressions | Associative Property of Addition |

(ab)c = a(bc) | (2x * 3y)(8) = (2x)(3y * 8) | Use this rule when multiplying three real numbers, variables, or algbraic expressions | Associative Property of Multiplication |

a(b + c) = ab + bc; (a + b)c = ac + bc | 3x(5 + 2x) = 3x * 5 + 3x * 2x; (y + 8)y = y * y + 8 * y | Use this rule when multiplying and adding three real numbers, variables, or algebraic expressions | Distributive Properties |

a + 0 = a | 5y^2 + 0 = 5y^2 | What happens when you try to add any number to 0? | Additive Identity Property |

a * 1 = a | (4x^2)(1) = 4x^2 | What happens when you multiply any number by 1? | Multiplicative Identity Property |

a + (-a) = 0 | 6x^3 + (-6x^3) = 0 | What happens when you try to add a number by its inverse? | Additive Inverse Property |

a * 1/a = 1, a /= 0 | (x^2 + 4)(1/(x^2 + 4)) = 1 | What happens when you try to multiply a term by its inverse form? | Multiplicative Inverse Property |