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

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

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

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

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)

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

3.) Factor

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

5.) Factor 6.) Factor

7.) Factor

Homework Practice Worksheet 6-4: Factoring