Simplifying Algebraic Expressions Flashcards

Study Notes

Algebraic Expressions

An algebraic expression consists of variables, numbers, and at least one operation (addition, subtraction, multiplication, or division).

Simplest Form

An algebraic expression is in simplest form if it contains no like terms and no parentheses.
The Distributive Property is used to combine like terms, which is known as simplifying the expression.

Distributive Property

Mathematically expressed as a(b + c) = ab + ac.
Example: 2(4 + 3) simplifies to 2(4) + 2(3).

Equivalent Expressions

Expressions that yield the same solutions are termed equivalent expressions.
Example: 2(x + 3) and 2x + 6 are equivalent.

Term

A term is defined as a number, a variable, or the product of a number and a variable.

Coefficient

A coefficient is the number or symbol that multiplies a variable or an unknown quantity in an algebraic term.

Like Terms

Like terms share the same variable and exponent, making them compatible for combining.

Constant

A constant is a term without a variable; constant terms are also considered like terms.

Identifying Parts of an Expression

Given the expression 6n - 7n - 4 + n:
- Terms: 6n, -7n, -4, n
- Coefficients: 6, -7, 1
- Like terms: 6n, -7n, n
- Constant: -4

Simplifying an Algebraic Expression

Simplifying involves writing the expression in a compact form by collecting like terms.
Only like terms can be combined, and the Distributive Property is essential for this process.
Example of simplification:
- Start with 7x - 2 - 7x + 6.
- Combine like terms: (7x - 7x) + (-2 + 6) leads to 0x + 4, ultimately simplifying to 4.

Description

Test your knowledge on simplifying algebraic expressions with these flashcards. Each card provides key terms and their definitions, helping you understand the concepts of variables, numbers, and operations in algebra. Perfect for students looking to reinforce their understanding of algebraic expressions.