Simplifying Algebraic Expressions

Distribution and Like Terms Section 4.2

Notes  When a ________ or ________ sign separates an algebraic expression into parts, each part is called a _______.

 The numerical factor of a term that contains a variable is called the ____________.

Notes  A term without a variable is called a _________.

 __________ terms contain the same variables to the same powers, such as 3x and 2x.

Like Terms  Like Terms have the EXACT same variables with the same exponents.

Like Terms 2x, -5x -8, 10 3y ², 8y² 7xy, -xy Unlike Terms 4x, 4y 9, 6x 5x, 5x² 3x²y, 8xy²

Examples  Identify the terms, like terms, coefficients, and constants  1. 4 – 4y + y – 3  2. 7 – 5y + 2 + 1

Example

 Find the like terms: 7x, -8, 4y, x, x ², 6, 5xy, 8y, 9

Notes  An algebraic expression is in _____________form if it has no like terms and no parentheses.

Combining Like Terms

 Terms must be

like

in order to add and subtract them.

 To combine like terms: 

Add

the coefficients  Keep the variable

Examples

6x + 5y – 3x + y -2x – 8y + 5x – 4y 5a – 2b + c – 5b + 4b

Distributive Property

 Signified by a number next to ( ) with no sign in between Ex: 5(x + 3)  Tells you to multiply the number outside by every term inside  Watch the signs

4(x + 3) (2y – 6)5 a(7b + 2c) -8(4m – 2n)

Examples

Simplifying Expressions o Distribute first (watch for sign of # you are distributing) o Combine like terms

Examples

3(x + 2) – 4x + 8 2 – 5(2x + 4) + x 2(3x – 4y) – (x – 2y)