Algebraic Expressions Flashcards

Coefficient

• A coefficient indicates the amount multiplied by a variable, e.g., in 3a, the coefficient of a is 3.

Difference

• The difference is the result of subtracting one number from another; for example, the difference between 8 and 2 is 6.

Factor

• A factor is a number that divides another number exactly, with 1 being a factor of all numbers; factors of 10 include 1, 2, 5, and 10.

Factor Pair

• Factor pairs consist of two factors that, when multiplied together, yield a particular product.

Highest Common Factor (HCF)

• The HCF of two numbers is the largest number that divides both; for instance, the HCF of 24 and 36 is 12.

Integer

• Integers are whole numbers, which can be positive, negative, or zero.

Perimeter

• The perimeter is the total distance around a shape, determined by adding the lengths of all its sides.

Powers

• Powers represent a number multiplied by itself a specified number of times.

Prime Number

• A prime number has exactly two factors: 1 and itself.

Product

• The product refers to the outcome of multiplying two numbers; for example, the product of 5 and 8 is 40.

Quadratic Equation

• A quadratic equation is one where the highest power of a variable is 2, e.g., 2x².

Sum

• A sum is the result of adding numbers together; for instance, the sum of 8 and 4 is 12.

Term

• Terms are the individual components of expressions or equations, like 7a or 4 in the expression 7a + 4.

Expressions and Equations

• In algebra, letters represent values that can change (variables) or unknown values. An expression combines terms using operations (+, -, ×, ÷), while an equation states that two expressions are equal.

Identical and Identity

• An identity is a true statement for all variable values; for example, 4a × a² = 4a³ is always true.

Rectangle Perimeter Example

• The perimeter of a rectangle can be calculated by adding the lengths of all sides: for width (x) and height (x - 3), it results in (4x - 6).

Simplifying Expressions

• Simplifying involves collecting like terms in an expression, such as combining 5a and 3a, or 2b and -6b for clarity and efficiency.