Choctaw High School Algebra I EOI Review POWERPOINT

Choctaw High School Algebra I EOI Review POWERPOINT OVERVIEW UNIT 1 LESSON 1. 1 – SIMPLIFYING EXPRESSIONS 1

SIMPLIFYING EXPRESSIONS To simplify an algebraic expressions, you need to combine the like terms. Like terms have the same variables with the same exponents. If two terms are like terms, then only their coefficients may differ. Once you find all the like terms, you can combine them by adding or subtracting the coefficients only. 2

ALGEBRAIC EXPRESSIONS An algebraic expression is a collection of real numbers, variables, grouping symbols and operation symbols. Here are some examples of algebraic expressions. 3

CONSIDER THE EXAMPLE: The terms of the expression are separated by addition. There are 3 terms in this example and they are. The coefficient of a variable term is the real number factor. The first term has coefficient of 5. The second term has an unwritten coefficient of 1. The last term , -7, is called a constant since there is no variable in the term. 4

Let’s begin with a review of two important skills for simplifying expression, using the Distributive Property and combining like terms. Then we will use both skills in the same simplifying problem. 5

DISTRIBUTIVE PROPERTY To simplify some expressions we may need to use the Distributive Property Do you remember it? Distributive Property a ( b + c ) = ba + ca 6

EXAMPLES Example 1: 6(x + 2) Distribute the 6. Example 2: -4(x – 3) Distribute the – 4. 6 (x + 2) = x(6) + 2(6) = 6 x + 12 -4 (x – 3) = x(-4) – 3(4) = -4 x + 12 7

PRACTICE PROBLEM Try the Distributive Property on -7 ( x – 2 ). Be sure to multiply each term by a – 7. -7 ( x – 2 ) = x(-7) – 2(-7) = -7 x + 14 Notice when a negative is distributed all the signs of the terms in the ( )’s change. 8

EXAMPLES WITH 1 AND – 1. Example 3: (x – 2) = 1( x – 2 ) Example 4: -(4 x – 3) = -1(4 x – 3) = x(1) – 2(1) = 4 x(-1) – 3(-1) =x - 2 = -4 x + 3 Notice multiplying by a 1 does nothing to the expression in the ( )’s. Notice that multiplying by a – 1 changes the signs of each term in the ( )’s. 9

LIKE TERMS Like terms are terms with the same variables raised to the same power. Hint: The idea is that the variable part of the terms must be identical for them to be like terms. 10

EXAMPLES Like Terms 5 x , -14 x Unlike Terms 5 x , 8 y -6. 7 xy , 02 xy The variable factors are identical. The variable factors are not identical. 11

COMBINING LIKE TERMS Recall the Distributive Property a (b + c) = b(a) +c(a) To see how like terms are combined use the Distributive Property in reverse. 5 x + 7 x = x (5 + 7) = x (12) = 12 x 12

EXAMPLE All that work is not necessary every time. Simply identify the like terms and add their coefficients. 4 x + 7 y – x + 5 y = 4 x – x + 7 y +5 y = 3 x + 12 y 13

COLLECTING LIKE TERMS EXAMPLE 14

BOTH SKILLS This example requires both the Distributive Property and combining like terms. 5(x – 2) – 3(2 x – 7) Distribute the 5 and the – 3. x(5) - 2(5) + 2 x(-3) - 7(-3) 5 x – 10 – 6 x + 21 Combine like terms. - x+11 15

SIMPLIFYING EXAMPLE 16

SIMPLIFYING EXAMPLE Distribute. 17

SIMPLIFYING EXAMPLE Distribute. 18

SIMPLIFYING EXAMPLE Distribute. Combine like terms. 19

SIMPLIFYING EXAMPLE Distribute. Combine like terms. 20