Algebraic Expressions Review Lesson

Algebraic Expressions

Algebraic Expressions: A Review

Let's review what we've learned so far about algebraic expressions.

●An algebraic expression is a mathematical phrase that

uses numbers, variables, and operation symbols.

○ 2x + 7 is an example of an algebraic expression

●A variable is a symbol that stands for one or more numbers.

○x, y, and n are examples of variables

Algebraic Expressions: A Closer Look

An algebraic expression can be broken into
different parts, including terms, variables,

coefficients, and constants.

An Algebraic Expression Dissected

5x + 3y -8

An Algebraic Expression Dissected

5x + 3y - 8

terms

(numbers, variables, or the product of a

number and a variable)

An Algebraic Expression Dissected

5x +3y - 8

coefficients

(numerical factors of a term, or the

number before a variable)

An Algebraic Expression Dissected

5x + 3y - 8

variables

(symbols that represent numbers that

are unknown or can change)

An Algebraic Expression Dissected

5x + 3y - 8

constant

(a term that has no variable, or a

number by itself)

Sage and Scribe Activity

Multiple Choice

The number before a variable is the _____.

• term

• constant

• coefficient

• variable

Multiple Choice

A letter that represents a number is called a _____.

• variable

• coefficient

• constant

• term

Multiple Choice

A number with no variable attached is called a  _____.

• coefficient

• constant

• variable

• term

Multiple Choice

What is the coefficient in the expression: 94a+2?

• 2

• 4

• 94

• 94a

Multiple Choice

What is the coefficient in this expression?
3x+4-2

• x

• 4

• 3x

• 3

Multiple Choice

How many terms are in the following expression?
 7y  + 3 - 7k  -2

• 2

• 7

• 4

• 3

Simplifying Algebraic Expressions

Combining Like Terms

Make it Simple!

To simplify an algebraic expression means to make it simpler.

In other words, rewrite the expression in the most compact
way, without changing the value of the expression. It's like
organizing the expression and making it neater!

Simplifying by Combining Like Terms

Like terms have exactly the same variable factors

Consider the following algebraic expression:

3a - 7 + 5b - 6a + 10 - 2b

Simplifying by Combining Like Terms

●Like terms have exactly the same variable factors

Consider the following algebraic expression:

3a - 7 + 5b - 6a + 10 - 2b

Simplifying by Combining Like Terms

●Like terms have exactly the same variable factors

Consider the following algebraic expression:

3a - 7 + 5b - 6a + 10 - 2b

Simplifying by Combining Like Terms

●Like terms have exactly the same variable factors

Consider the following algebraic expression:

3a - 7 + 5b - 6a + 10 - 2b

Simplifying by Combining Like Terms

To add the like terms, simply add the coefficients.

3a - 7 + 5b - 6a + 10 - 2b

-3a

Simplifying by Combining Like Terms

To add the like terms, simply add the coefficients.

3a - 7 + 5b - 6a + 10 - 2b

-3a +3b

Simplifying by Combining Like Terms

To add the like terms, simply add the coefficients.

3a - 7 + 5b - 6a + 10 - 2b

-3a +3b+ 3

Multiple Choice

Simplify the expression: 3x + 2x

• 5x

• x

• 6x

• 5

Multiple Choice

Simplify the expression: 7v + 2 + 12 + 2v

• 23

• 23v

• 9 + 14v

• 9v + 14

Multiple Choice

Simplify the expression: 2x + 1 + 7x 

• 10x

• 10

• 9x + 1

• 9 + 1x

Multiple Choice

Simplify the expression: 2x + 1 + 7x 

• 10x

• 10

• 9x + 1

• 9 + 1x

Multiple Choice

Simplify the following expression
7 - 8c + 3 - 6c 

• -10+14c

• -25

• 10-14c

• 25c

Multiple Choice

-6k + 7k=

• k

• -k

• 12k

• -12k

Multiple Choice

Simplify by combining like terms:
5a + 2b - 3a + 4

• 8a + 2b + 4

• 2a + 2b + 4

• 8ab

• 4ab + 4