1. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Page 256 3)
(x + 1)(x + 5) 7)
Prime
11)
(x – 9)(x + 2)
15)
(x + 6)(x – 6)
19)
(x + 4)(x + 4) or (x + 4)2
23)
(z – 11)(z + 11)
25)
{5, 6}
27)
{+7}
29)
(–4, –1}
31)
{–5 DR}
33)
{–6, 9}
35)
{–9, 0}
37)
{7 DR}
39)
It was factored wrong; it should be (x + 2)(x – 3) = 0
41) A
43)
3(10)(12) or 360 = (x + 10)(x + 12)
57)
x2 – 19x + 88 = 0
61)
3, ext: –10
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4.4: Sum and Difference of Perfect Cubes and Special Factoring 1

2. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Page 263 3)
(2x + 3)(x + 1) 7)
(11z – 9)(z + 1)
11)
(7m – 3)(2m + 1)
15)
(7n – 4)(7n + 4)
19)
(3p – 2)2
23)
2(3z + 4)(3z + 2)
25)
6u(u – 4)
27)
4(5x + 1)(x + 6)
29)
–3(6n – 5)(2n – 1)
33)
{–2, 2}
37)
{–3/2 DR}
41)
{–1/4, 5}
45)
{–3/11, 2}
49)
{–1, 7/12}
53)
{–1, 8/3}
57)
{0, 4}
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4.4: Sum and Difference of Perfect Cubes and Special Factoring 2

3. Sum and Difference of Perfect Cubes and Special Factoring
SECTION 4.4a
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

4. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Factor Flowchart
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

5. SUM & DIFFERENCE IN CUBES
Take the GCF Out
Put the equation into perfect cubes
Put the bases of the cubes into parentheses
Refer to the bases in the parentheses and follow the format of S1OMAS2
S1 – Square the first base
O – Take Opposite of the original problem’s sign
M – Multiply the first and second base (leave the signs alone)
A – Put addition sign
S2 – Square the second base
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

6. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
CUBE ROOTS
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

7. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
EXAMPLE 1
Factor x3 – 27
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

8. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
EXAMPLE 1
Factor x3 – 27
S1 – Square the first base
O – Take Opposite sign
M – Multiply the first & second base
A – Put addition sign
S2 – Square the second base
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

9. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
EXAMPLE 1
Factor x3 – 27
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

10. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
EXAMPLE 2
Factor x3 + 64
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

11. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Your Turn
Factor x3 – 1000
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

12. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Example 3
Factor 27x
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

13. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
EXAMPLE 4
Factor x6 – 1
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

14. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Your Turn
Factor 4x5 – 32x2
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

15. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Example 5
Factor x4 + 5x2 + 6
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

16. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Example 6
Factor x4 – 2x2 – 8
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

17. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Your Turn
Factor x4 – 5x2 – 36
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4.4: Sum and Difference of Perfect Cubes and Special Factoring

18. 4.4: Sum and Difference of Perfect Cubes and Special Factoring
Assignment
WKST
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4.4: Sum and Difference of Perfect Cubes and Special Factoring