1. Difference of Squares Chapter 8.8

2. Difference of Squares (Definition)

3. Factor m 2 – 64. m 2 – 64 = m 2 – 8 2 Write in the form a 2 – b 2. = (m + 8)(m – 8)Factor the difference of squares. Answer: (m + 8)(m – 8) Difference of Squares Ex#1

4. Factor 16y 2 – 81z 2. 16y 2 – 81z 2 = (4y) 2 – (9z) 2 Write in the form a 2 – b 2. = (4y + 9z)(4y – 9z)Factor the difference of squares. Answer: (4y + 9z)(4y – 9z) Difference of Squares Ex#2

5. A.(5a + 6b)(5a – 6b) B.(5a + 6b) 2 C.(5a – 6b) 2 D.25(a 2 – 36b 2 ) Factor the binomial 25a 2 – 36b 2. Difference of Squares - Your Turn!

6. Factor 3b 3 – 27b. If the terms of a binomial have a common factor, the GCF should be factored out first before trying to apply any other factoring technique. = 3b(b + 3)(b – 3)Factor the difference of squares. 3b 3 – 27b = 3b(b 2 – 9)The GCF of 3b 2 and 27b is 3b. = 3b[(b) 2 – (3) 2 ]Write in the form a 2 – b 2. Answer: 3b(b + 3)(b – 3) Difference of Squares with a GCF Ex#1

7. Factor 9x 5 – 36x. Answer: 9x(x 2 – 2)(x 2 + 2) 9x 5 – 36x= 9x(x 4 – 4)Factor out the GCF. = 9x[(x 2 ) 2 – 2 2 ]Write x 2 – 4 in a 2 – b 2 form. = 9x(x 2 – 2)(x 2 + 2)Factor the difference of squares. Difference of Squares with a GCF Ex#2

8. A.3x(x 2 + 3)(x 2 – 4) B.3x(x 2 + 2)(x 2 – 2) C.3x(x 2 + 2)(x + 2)(x – 2) D.3x(x 4 – 4x) Factor 3x 5 – 12x. Difference of Squares with a GCF – Your Turn!

9. Factor 256 – n 4. 256 – n 4 = 16 2 – (n 2 ) 2 Write 256 – n 4 in a 2 – b 2 form. = (16 + n 2 )(16 – n 2 )Factor the difference of squares. = (16 + n 2 )(4 2 – n 2 )Write 16 – n 2 in a 2 – b 2 form. = (16 + n 2 )(4 – n)(4 + n)Factor the difference of squares. Answer: (16 + n 2 )(4 – n)(4 + n) Difference of Squares with 2 “Differences”

10. A.(9 + d)(9 – d) B.(3 + d)(3 – d)(3 + d)(3 – d) C.(9 + d 2 )(9 – d 2 ) D.(9 + d 2 )(3 + d)(3 – d) Factor 81 – d 4. Difference of Squares with 2 “Differences” – Your Turn!

11. Factor 6x 3 + 30x 2 – 24x – 120. 6x 3 + 30x 2 – 24x – 120Original polynomial = 6(x 3 + 5x 2 – 4x – 20)Factor out the GCF. = 6[(x 3 – 4x) + (5x 2 – 20)]Group terms with common factors. = 6[x(x 2 – 4) + 5(x 2 – 4)]Factor each grouping. = 6(x 2 – 4)(x + 5)x 2 – 4 is the common factor. = 6(x + 2)(x – 2)(x + 5)Factor the difference of squares. Answer: 6(x + 2)(x – 2)(x + 5) Difference of Squares Extended Example

12. A.5(x 2 – 9)(x + 5) B.(5x + 15)(x – 3)(x + 5) C.5(x + 3)(x – 3)(x + 5) D.(5x + 25)(x + 3)(x – 3) Factor 5x 3 + 25x 2 – 45x – 225. Difference of Squares Extended Example – Your Turn!

13. HOMEWORK 8.8 #’s 15-44 all