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

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

Example Find 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 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

Examples 4(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

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