Algebra Foundations Study Notes

Algebra Foundations Study Notes

• Distributive Property: This property states that multiplying a number by a sum is the same as multiplying each addend individually and then summing the results. Represented mathematically as A(B + C) = AB + AC.

• Equivalent Expressions: These are expressions that yield the same numerical value for all variable assignments, indicating they represent the same mathematical relationship or quantity.

• Algebraic Expression: A type of mathematical phrase that includes at least one variable, and may also incorporate numbers and operation symbols, such as addition or multiplication.

• Numeric Expression: A mathematical sentence comprised solely of numbers and one or more operation symbols, excluding any variables.

• Commutative Property: This property indicates that the order of addition or multiplication does not affect the sum or product. For addition, it is expressed as a + b = b + a.

• Associative Property: This property reveals that the way numbers are grouped in addition or multiplication does not change their sum or product. For addition, shown as (a + b) + c = a + (b + c).

• Variable: A variable is a symbol (typically a letter) representing a quantity that can vary or change in value.

• Formula: A mathematical expression that combines numbers and symbols to convey a specific calculation or relationship between quantities.

• Square Number: A number resulting from multiplying a number by itself, such as 4 (which is 2 squared).

• Square Root: The square root of a number is the value that, when multiplied by itself, returns the original number; for example, the square root of 9 is 3.

• Pythagorean Theorem: A fundamental principle in geometry that relates the lengths of the sides of a right triangle, expressed mathematically as a² + b² = c², where c represents the hypotenuse.

• Hypotenuse: In a right triangle, the hypotenuse is the longest side, opposite the right angle.

• Cubic Number: This refers to a number that comes from multiplying a number by itself twice. For example, 27 is a cubic number since it is derived from 3 x 3 x 3.

• Cube Root: The cube root of a number is the value that, when multiplied by itself three times, gives the original number; for example, the cube root of 64 is 4.

• Exponent: An exponent indicates how many times a base number is to be multiplied by itself. For example, in 2^3 (2 raised to the power of 3), 2 is multiplied by itself three times (2 x 2 x 2).