Simplifying Algebraic Expressions

1. Simplifying Algebraic Expressions Distribution and Like Terms Section 5.5

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 ____________.

3. Notes • A term without a variable is called a _________. • __________ terms contain the same variables to the same powers, such as 3x and 2x.

4. Like Terms • Like Terms have the EXACT same variables with the same exponents. Like TermsUnlike Terms 2x, -5x 4x, 4y -8, 10 9, 6x 3y², 8y² -5x, 5x² 7xy, -xy 3x²y, 8xy²

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

6. Example • Find the like terms: 7x, -8, 4y, x, x², 6, 5xy, 8y, 9

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

8. Combining Like Terms • Terms must be like in order to add and subtract them. • To combine like terms: • Add the coefficients • Keep the variable

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

10. 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

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

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

13. Examples 3(x + 2) – 4x + 8 2 – 5(2x + 4) + x 2(3x – 4y) – (x – 2y)