Basic Algebra and Algebraic Manipulation

These flashcards cover key vocabulary and concepts related to basic algebra and algebraic manipulation as discussed in the lecture notes.

Variable

A letter used to represent a number in algebra.

Coefficient

A numerical factor multiplied by a variable in an algebraic expression.

Algebraic Expression

An expression that includes numbers, variables and operation symbols, without an equality sign.

Linear Expression

An algebraic expression in which the highest power of the variable is one.

Non-linear Expression

An algebraic expression that includes terms with powers greater than one and/or products of variables.

Evaluating an Expression

Finding the numeric value of an algebraic expression when the variables have specific values.

Distributive Law

A property indicating that multiplying a number by a sum is the same as multiplying each addend separately and then adding results.

Factorization

The process of breaking down an algebraic expression into products of factors.

Like Terms

Terms that contain the same variables raised to the same powers.

Unlike Terms

Terms that do not have the same variable components.

Addition of Linear Expressions

Combining like terms from linear expressions to form a new linear expression.

Subtraction of Linear Expressions

The process of subtracting like terms from each other within linear expressions.

Algebraic Notation

The symbolic representation of mathematical concepts and operations.

Index

The power to which a number or variable is raised in an expression.

Variable 🧁

A letter used to represent a number in algebra.\n\nExample: In the expression 2x + 7, the variable is x. 🌸

Coefficient 🍭

A numerical factor multiplied by a variable in an algebraic expression.\n\nExample: In 5y, the coefficient is 5. 🎀

Algebraic Expression 🍬

An expression that includes numbers, variables and operation symbols, without an equality sign.\n\nExample: 3a + 2b - 1. ☁️

Linear Expression 🍡

An algebraic expression in which the highest power of the variable is 1.\n\nExample: x + 10. ✨

Non-linear Expression 🍰

An algebraic expression that includes terms with powers greater than 1 and/or products of variables.\n\nExample: x^{2} - 5. 🍓

Evaluating an Expression 🌷

Finding the numeric value of an algebraic expression when the variables have specific values.\n\nExample: To evaluate x + 4 for x = 3, we calculate 3 + 4 = 7. 🍼

Distributive Law 🍮

A property indicating that multiplying a number by a sum is the same as multiplying each addend separately and then adding results.\n\nExample: a(b + c) = ab + ac. 🧸

Factorization 🩰

The process of breaking down an algebraic expression into products of factors.\n\nExample: 2x + 4 = 2(x + 2). 🎀

Like Terms 🍓

Terms that contain the same variables raised to the same powers.\n\nExample: 3x and 5x are like terms. ☁️

Unlike Terms 🍭

Terms that do not have the same variable components.\n\nExample: 4x and 4y are unlike terms. 🧁

Addition of Linear Expressions 🌸

Combining like terms from linear expressions to form a new linear expression.\n\nExample: (x + 2) + (2x + 3) = 3x + 5. ✨

Subtraction of Linear Expressions 🍼

The process of subtracting like terms from each other within linear expressions.\n\nExample: (5x + 7) - (2x + 3) = 3x + 4. 🌷

Algebraic Notation ☁️

The symbolic representation of mathematical concepts and operations.\n\nExample: Writing 'three times x' as 3x. 🍡

Index 🍰

The power to which a number or variable is raised in an expression.\n\nExample: In x^{3}, the index is 3. 🍩