1. Sum/Diff Cubes and PST
Brett Solberg AHS ‘11-’12

2. Factor the Following 1) 3x2y + 18xz 2) 49x2 – 9y2 3) 3x2 - 147
We will review a few problems from each section.

3. Today’s Agenda Factor By: Greatest Common Factor GCF
Difference of Squares
Sum and Difference of Cubes
Perfect Square Trinomials

4. Factoring Sum/Difference of Cubes
a3 + b3 = (a + b)(a2 – ab + b2)
8 + y3
a = 2 b = y
(2 + y)(4 – 2y + y2)
a3 - b3 = (a - b)(a2 + ab + b2)
27x3 – 64
a = 3x b = 4
(3x – 4)(9x2 + 12x + 16)

5. When to use Sum/Diff Cubes
Binomial
Subtraction or Addition
Perfect Cubes

6. Examples
1) x3 – 1 a = x b = 1 (x – 1)(x2 + x + 1) 6) 1000x3 – 27 a = 10x b = 3 (10x – 3)(100x2 + 30x – 729) 9) 54y4 – 128y 2y(27y3 – 64) a = 3y b = 4 2y(3y – 4)(9y2 + 12y + 16)

7. Perfect Square Trinomials PST
(a + b)2 = a2 + 2ab + b2
(2x + 1)2 = 4x2 + 4x + 1
(a – b)2 = a2 – 2ab + b2
(2x – 5)2 = 4x2 – 20x + 25

8. When to use Perfect Square Trinomials
First and last terms perfect squares
Middle term twice the product of the square roots of outside terms.

9. Examples
1) 4x2 + 20x + 25 a = 2x b = 5 (2x + 5)2 8) x2 – 18x + 81 a = x b = 9 (x – 9)2 15) 5x2 – 30x (x2 – 6x + 9) 5(x – 3)2

10. Class Assignment Sum/Diff of Cubes Worksheet
Perfect Square Trinomial Worksheet