Algebra is based of five fundamental laws, which govern the operations of addition, subtraction, multiplication, and division. Each of the laws is expressed in letters variables. Where variables a, b and c are all real numbers, any number can be substituted for a variable without conflicting with the way the rule works.

The Commutative Law of Addition: a + b = b + a. Under this law, the order in which two numbers are added has no bearing on the sum derived.

The Associative Law of Addition:  a + (b + c) = (a + b) + c. Under this law, it does not matter which combination of numbers are added first, the sum remains the same.

The Commutative Law of Multiplication: ab = ba. Under this law, it does not matter which order numbers are multiplied in, the product is the same.

The Associative Law of Multiplication:  a * (bc) = (ab) * c. Under this law, numbers can be multiplied in any sequence without affecting the final product.

The Distributive Law of Multiplication Over Addition: a (b + c) = ab + ac. Under this law, if a number multiplies a sum, the total is the same as the sum of the separate products of the multiplier and each of the addends represented by b and c.

The Quadratic Equation: Another key algebraic equation is the quadratic equation, in which the highest power to which the unknown quantity is raised is the second.


Without algebra, civilization wouldn't exist. Illustration: Megan Jorgensen