1. Factoring GCF and Binomials
Section 5.4(a)
Factoring GCF and Binomials

2. Number of Terms Method Any Greatest Common Factor Two
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Three
Perfect Square Trinomials
General Trinomials
Four or More
Grouping

3. I. Greatest Common Factor
Identify all common factors and factor out
the GCF or greatest common factor
1.) Factor: (16x3 - 32x2y + 8xy2)
2•8•x•x•x - 4•8•x•x•y + 8•x•y•y

4. II. Difference of two squares
(a - b)(a + b)
(a2 - b2)
Steps to follow the pattern:
1. Find the square roots a2 = a and b2 = b
Separate into parentheses (a - b)(a + b)
Signs one of each
2.)
Factor

5. Difference of perfect cubes
THE DIFFERENCE OF TWO CUBES
Explain why a 3 – b 3 =
Volume of solid I
Volume of solid II
Volume of solid III 1
For each of solid I, solid II, and solid III, write an algebraic expression for the solid’s volume. 2
a 2(a – b)
a b(a – b)
b 2(a – b)
Substitute your expressions from Step 2 into the equation from Step 1. Use the resulting equation to factor a 3 – b 3 completely. 3
a 3 – b 3 =
Volume of solid I
Volume of solid II
Volume of solid III
a 2(a – b)
b 2(a – b)
a b(a – b)
a 3 – b 3 = (a – b)(a 2 + a b + b 2)

6. III. Sum of Two cubes
(a + b)(a2 - ab + b2)
(a3 + b3)
Steps to follow the pattern:
Find the cube roots a3 = a and b3 = b
Separate into first parentheses (a + b)(a2 - ab + b2)
Square the first one (a + b)(a2 - ab + b2)
3. Multiply cube roots together (a + b)(a2 - ab + b2)
Square the second one (a + b)(a2 - ab + b2)
Signs stay the same, changes, then is positive

7. 3.)
Factor

8. VI. Difference of Two cubes
(a3 - b3)
(a - b)(a2 + ab + b2)
4.)
Factor

9. 5.)
Factor
6.)
Factor

10. 7.)
Factor

11. Homework
Practice Worksheet 6-4: Factoring