Simplifying Algebraic Expressions

Distribution and Like Terms

Section 5.5

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 Unlike Terms2x, -5x 4x, 4y-8, 10 9, 6x3y², 8y² -5x, 5x²7xy, -xy 3x²y, 8xy²

ExamplesIdentify the terms, like terms, coefficients,

and constants

1. 4 – 4y + y – 3

2. 7 – 5y + 2 + 1

ExampleFind the like terms:

7x, -8, 4y, x, x², 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 coefficientsKeep the variable

Examples6x + 5y – 3x + y

-2x – 8y + 5x – 4y

5a – 2b + c – 5b + 4b

Distributive PropertySignified 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

Examples4(x + 3)

(2y – 6)5

a(7b + 2c)

-8(4m – 2n)

Simplifying Expressions

oDistribute first (watch for sign of # you are distributing)

oCombine like terms

Examples3(x + 2) – 4x + 8

2 – 5(2x + 4) + x

2(3x – 4y) – (x – 2y)