CPM Algebra Chapter 3 Flashcards

Algebra Tiles

• Algebra tiles are manipulatives representing constant or variable quantities through area.
• Tiles include large squares (x², y²), rectangles (x-by-1, y-by-1, x-by-y), and unit tiles (1-by-1).
• Positive quantities are represented by shaded tiles, while unshaded tiles indicate negative quantities.

Binomial

• Defined as an expression consisting of the sum or difference of exactly two terms.
• Example: −2x + 3y² qualifies as a binomial.

Distributive Property

• Allows expression products to be expressed as sums of terms.
• Formula: a(b + c) = ab + ac. Example: 2(x + 4) becomes 2x + 8 using this property.
• Can be demonstrated using algebra tiles or a generic rectangle.

Legal Moves

• "Legal" moves maintain the equality of expressions on both sides of an equation mat.
• Examples include removing identical tiles from both sides to preserve equality.

Exponent

• In expressions of the form b^a, 'a' is called the exponent specifying how many times the base (b) is multiplied by itself.
• Exponential rules: x^0 = 1 for any non-zero x; negative exponents indicate reciprocals, e.g., x^(-n) = 1/x^n.

Integers

• Defined as the set {...−3, −2, −1, 0, 1, 2, 3,...}, encompassing positive and negative whole numbers and zero.

Polynomial

• An expression formed by the sum or difference of two or more monomials.
• Example: x⁸ - 4x⁶y + 6x⁴y² is classified as a polynomial.

Solve

• Refers to finding all solutions to equations or inequalities.
• Example: Solving x² = 9 results in solutions x = 3 and x = −3.
• An equation can be manipulated to express a variable in terms of others, e.g., from 2y − 8x = 16 to y = 4x + 8.

Term

• A term may be a single number, variable, or products of numbers and variables.
• Terms in the expression 1.2x - 45 + 3xy² are 1.2x, -45, and 3xy².

Area

• In math, area measures the number of square units needed to fill a flat region.
• The concept of area extends to more complex surfaces in advanced study.

Closed Sets

• A numerical set is closed under an operation if applying the operation to any two numbers within the set results in a number still within the set.
• Example: Whole numbers are closed under addition but not under division.

Expression

• An expression consists of individual terms combined by plus or minus signs, lacking an "equals" component.
• Numerical expressions involve only numbers, while algebraic expressions incorporate variables (e.g., y - 3/4 + x).

Product

• The outcome of multiplying two or more values.
• Example: The product of 4 and 5 equals 20; multiplying 3a and 8b² yields 24ab².

Standard Form

• The standard form for a linear equation is expressed as ax + by = c, where a, b, and c are real numbers, and not both a and b can be zero.
• Example: 2.5x − 3y = 12 is in standard form.