Simplifying Algebraic Expressions by Combining Like Terms Lesson

Simplifying Algebraic Expressions by Combining Like Terms Lesson 6. 2. 3 6. EE. 2 b, 6. EE. 3, 6. EE. 4

In Chapter 4 We learned… • A variable is a letter that stands for an unknown number. • Different letters indicate different values. For example, if X = 5, then the value of Y and Z will be a number other than 5.

In Chapter 4… • We learned that an algebraic expression is a mathematical expression built from numbers, variables, and operations. • There are no equal signs in an algebraic expression. Example 4 x + y + 9 + x²

Today… 1) We are going to learn about the parts that make up an algebraic expression. 2) We are also going to learn how to simplify an algebraic expression by… “combining like terms”

Let’s Get Started… q Section 1 – Vocabulary q Section 2 – “Like” Terms q Section 3 – Simplifying Expressions by combining the “like” terms

Terms 4 x + y + 9 – x 2 o Terms are the small parts (or chunks) that make up an expression. o This expression has 4 terms. Do you notice anything that might help you identify where each new term starts? Terms are separated by either a + or – sign!

How many terms are in this expression? 9 x – 5 + x 2 Answer: 3

Coefficient: 5 x + y + 8 o A coefficient is the number that multiplies the variable. o ALL variables have a coefficient. If you don’t see a number in front of the variable, it is assumed to be 1. 5 is the coefficient in front of the x 1 is the coefficient in front of the y

Constant o A constant is a term that has no variable. o It is the plain number. 5 x + y + 8 Constants are constantly alone!

Naming Coefficients and Constants When naming coefficients and constants, the sign directly in front goes with it. 3 m – 2 n + n – 4 Coefficients: 3 -2 1 Constants: -4

Name the item in blue x + 5 x – 2 + y 3 Choose one… A) coefficient B) term C) constant

Name the item in blue 12 + k 3 Select all that apply… A) coefficient B) variable C) constant D) term

Write a word to describe the blue item. 7 a 2 + 3 b – 1 term

-m – 12 + 4 n 1) How many terms are there? 3 2) Name the coefficients: -1 4 3) Name the constants: -12

Moving On… q Section 1 – Vocabulary q Section 2 – “Like” Terms q Section 3 – Simplifying Expressions by combining the “like” terms

What are “Like” Terms? 5 x and 10 x n 2 and 7 n 2 14 and 19 Like Terms are terms that have the same variable and exponent.

Are these like terms? 6 b and 9 b Yes, they have the same variable and exponent.

Are these like terms? 5 x and 2 y No, they do not have the same variable.

Are these like terms? x 2 and 8 x 2 Yes, they have the same variable and exponent.

Are these like terms? 7 x and 5 x² No, they do not have the same exponent.

Are these like terms? 6 and 15 Yes, they are both constants.

Are these like terms? 3 x and 1 No, they do not have the same variable.

Are these like terms? 2 m and 6 m Yes, they have the same variable and exponent.

Moving On… q Section 1 – Vocabulary q Section 2 – “Like” Terms q Section 3 – Simplifying Expressions by combining the “like” terms

Steps for Simplifying an Algebraic Expression Step 1 Use the Distributive Property to remove any parentheses Step 2 Identify the “like” terms Step 3 Combine the “like” terms by adding or subtracting the coefficients 3(x + 5) + 4 x 3 x + 15 + 4 x 3 x + 4 x 7 x + 15 Answer: 7 x + 15