How do you simplify algebraic expressions?

For example, how can you simplify 5 + x + 2x + 8 ?

In this lesson you will learn how to simplify algebraic

expressions by combining like terms.

Let’s ReviewLet’s Review

We know that algebraic expressions contain numbers, operations and at

least one variable. 2(x + 3)

4a-3 15 ÷ y

12 - w2

Let’s ReviewLet’s Review

The Any Order, Any Grouping Property states that numbers can be added in any order or multiplied in any order without

changing the sum or product.

For example:5 + x = x + 5

3 • (2 • 4) = (3 • 2) • 4

Let’s ReviewA Common Mistake

Combining x2 and x terms.

Let’s ReviewCore Lesson

5 + x + 2x + 8How many terms?- - - -

An expression is made up of “terms.” A term is either a number or a variable or

a number and variable multiplied together. Terms are separated by the operations of addition and subtraction.

Let’s ReviewCore Lesson

If a term contains a variable, it also has a “coefficient.”

2x

coefficient variableA coefficient tells you how many times

the variable is used as an addend.

is the same as x + x

Let’s ReviewCore Lesson

5 + x + 2x + 8

Which of these terms can you group together?

3x + 13 is equivalent to 5 + x + 2x + 8

Let’s ReviewCore Lesson

Let’s combine these like terms:

x2 + x2 + 2x2 is equivalent to

x + 3x+ x + 2x is equivalent to

4x2

7x

1 + 10 + 39 + 5 is equivalent to55

Remember: The coefficient of a variable is 1 if there is no other listed.

In this lesson you have learned to write equivalent algebraic

expressions by combining like terms.

Let’s ReviewGuided Practice

Simplify this algebraic expression by combining like terms:5 + 3x + x2 + 4x + 2x2

Let’s ReviewExtension Activities

Simpify this algebraic expression:

2 + 2x + 4x + 5 + 3x2 + 2x2

Let’s ReviewExtension Activities

Simplify the algebraic expression.

x3 + 3x3 + 2x2 + 6x2 + 4 x + 12x + 5

Let’s ReviewQuick Quiz

Write an equivalent expression combining like terms for 3a + a + 5.

Write an equivalent expression combining like terms for 10 + p + p2 + 5p2