This document discusses algebraic expressions and how to work with them. It defines an expression as a symbol or combination of symbols that represents a value or relation. It explains how to write verbal and symbolic expressions, calculate the value of an expression by plugging in numbers, and factor expressions by finding the greatest common factor or grouping terms. Examples are provided for each concept to illustrate the process. Resources for further information on algebraic expressions are listed at the end.

1. Jessica Francis

2. Algebraic Expressions

Write a verbal expression.
Write an expression in symbolic
form.
Calculate the answer of an
expression.
Factor an expression.

3. What is an Expression?

Expression
A symbol or combination of symbols.
It represents a value or relation.
Verbal Expression
Example- Three x plus two y equals
zero.

4. What is an Expression?

Symbolic Expression
Example- 3x+2y=8.
Calculate an Expression
Plug in numbers for variables.

5. Verbal Expression

Represents
numbers, symbols, and letters.
Example- 2x+3(y+1)=4
= Two x plus three times the
quantity of y plus one
equals four.

6. Symbolic Expression

Represents words/verbal
expressions.
Example- Three x minus five y equals
twelve.
= 3x-5y=12

7. Calculating

Given values for variables.
Given expression.
So…
Plug values into the expression.
Solve.

8. Calculating

Example- f(x)=5x-2y
Evaluate the expression when x=4 &
y=8.
=5(4) - 2(8)
= 20 – 16
=4

9. Factor Expressions

Greatest Common Factor
15 - 5x3 GCF
45 – 5x3x3 = 5x3
Grouping
2x^3+4x^2+4x-8
(2x^3+4x^2)+ (4x-8)

10. Greatest Common Factor

Look for a GCF.
Turn the equation into…
GCF x ( )
Make it look like a multiplication
problem.

11. GCF

Example-
2x^2y^2+4x^2
GCF= 2x^2
2x^2(y^2 + 2)
Example-
3y^2 – 3
GCF= 3
3(y^2 - 1)

12. Grouping

Group first 2 terms together.
Group last 2 terms together.
Factorindividually using GCF.
Combine the terms.

13. Grouping

Example-
X^3-3x^2+2x-6
(X^3-3x^2) + (2x-6)
X^2(x-3) + 2(x-3)
(X^2+2)(x-3)

14. Review

Write in Symbolic Form
Four x minus three y equals twenty-
four.
4x-3y=24
Write in a Verbal Expression.
3x+2z=45
Three x plus two z equals forty-five.

15. Review

Calculate the answer.
5x-6y=? when X=5 & Y=3
5(5)-6(3)= 25-18
=7
What is the GCF of…
15x^2+3x? 25y^3-5y^2
=3x. =5y^2

16. Review

Factor the expression.
x^3+4x^2
=x^2(x+4)
x^3 – 4x^2 + 4x – 16
(x^3 – 4x^2)+(4x-16)
x^2(x-4)+4(x-4)
(x^2+4)(x-4)

17. Resources

Spector, Lawrence. "The Math Page."
Skill in Algebra. Lawrence
Spector, 2004-2010. Web. 1 Oct 2010.
<http://www.themathpage.com/alg/al
gebra.htm>.
Stewart, James, LotharRedlin, and
Saleem Watson. College Algebra. 5th.
Belmont, CA: Brooks/Cole, 2009. 32-
45. Print.