Section 5.4(a)

Factoring GCF and Binomials

Number of Terms

Any • Greatest Common Factor

Method

Two • Difference of Two Squares• Sum of Two Cubes• Difference of Two Cubes

Three • Perfect Square Trinomials• General Trinomials

Four or More • Grouping

I. Greatest Common Factor

1.) Factor: (16x3 - 32x2y + 8xy2) 2•8•x•x•x - 4•8•x•x•y + 8•x•y•y

Identify all common factors and factor out the GCF or greatest common factor

(a2 - b2) (a - b)(a + b)

2.) 92 xFactor

II. Difference of two squares

Steps to follow the pattern:1. Find the square roots a2 = a and b2 = b2.Separate into parentheses (a - b)(a + b)3.Signs one of each

THE DIFFERENCE OF TWO CUBES

1 Explain why a 3 – b

3 = + + .Volume of solid I

Volume of solid II

Volume of solid III

2 For each of solid I, solid II, and solid III, write an algebraic expression for the solid’s volume.

3Substitute your expressions from Step 2 into the equation from Step 1. Use the resulting equation to factor a 3 – b 3 completely.

a 2(a – b) a b(a – b) b 2(a – b)

a 3 – b

3 = + +

Volume of solid I

Volume of solid II

Volume of solid III

a 2(a – b) a b(a – b) b 2(a – b)

a 3 – b

3 = (a – b)(a 2 + a b + b

2)

Difference of perfect cubes

(a3 + b3) (a + b)(a2 - ab + b2)

Steps to follow the pattern:1.Find the cube roots a3 = a and b3 = b2.Separate into first parentheses (a + b)(a2 - ab + b2)3.Square the first one (a + b)(a2 - ab + b2)3. Multiply cube roots together (a + b)(a2 - ab + b2)4.Square the second one (a + b)(a2 - ab + b2)5.Signs stay the same, changes, then is positive

III. Sum of Two cubes

Factor3.) 83 x

Factor

(a3 - b3) (a - b)(a2 + ab + b2)

4.) 278 3 a

VI. Difference of Two cubes

Factor

Factor5.)

512125 3 a6.)

aay 273 2

Factor7.) 22 2516 yx

Homework

Practice Worksheet 6-4: Factoring