The document provides instructions for factorizing cube expressions using the difference of cubes formula. It explains that to factor expressions of the form x3 ± a, you take the cube roots of the first and last terms to write as the first factor, and then generate the second factor by squaring the first term of the first factor, taking the opposite of the product of the first two terms, and squaring the last term. It provides examples of factorizing expressions like x3 + 8, 8a3 + 64, and x3 - 8 using this process.

6. (x3 + y3) = (x + y)(x2 – xy + y2 )

7. 1. Factor x3 + 8
1. Find the cube roots of the first and
last terms
8
x3
First Term: = x
Second Term: = 2

8. 1. Factor x 3 + 8
2. Write their sum as the first
factor.
(x + 2)

9. 1. Factor x 3 + 8
3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(x + 2) ( )
x2 -2x + 4

10. Factor 8a3 + 64
1. Find the cube roots of the first and
last terms?
64
8a3
First Term: = 2
Second Term: = 4
a

11. 2. Write their sum as the first
factor.
(2a + 4)
Factor 8a3 + 64

12. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(2a + 4)( )
4a2 -8a + 16
Factor 8a3 + 64

13. Factor 27a6 + 216b3
1. Find the cube roots of the first and
last terms?
216b3
27a6
First Term: = 3
Second Term: = 6
a2
b

14. 2. Write their sum as the first
factor.
Factor 27a6 + 216b3
3a2 + 6b

15. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
( )
9a4-18a2b
3a2 + 6b + 36b2
Factor 27a6 + 216b3

16. (x3 - y3) = (x - y)(x2 + xy + y2 )

17. Factor x 3 - 8
1. Find the cube roots of the first and
last terms?
8
x 3
First Term: = x
Second Term: = 2

18. Factor x 3 - 8
2. Write their difference as the
first factor.
(x - 2)

19. Factor x 3 + 8
3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Adding the product of the first and
second terms of the first factor; c. Squaring
the last term of the first factor
(x - 2) ( )
x2 + 2x + 4

20. Factor 8a3 - 64
1. Find the cube roots of the first and
last terms?
64
8a3
First Term: = 2
Second Term: = 4
a

21. 2. Write their sum as the first
factor.
(2a - 4)
Factor 8a3 - 64

22. 3. For the second factor, get the trinomial
factor by: a. Squaring the first term of the first
factor; b. Subtracting the product of the first
and second terms of the first factor; c.
Squaring the last term of the first factor
(2a - 4) ( )
4a2 +8a+ 16
Factor 8a3 - 64

23. 1. Find the cube roots of the first and last terms
2. Write their sum as the first factor.
3. For the second factor, get the trinomial factor
by:
a. Squaring the first term of the first factor;
b. Subtracting the product of the first and second
terms of the first factor;
c. Squaring the last term of the first factor

24. Find the Factors of the following
1. b3 - 343 2. 8c3 + 125
3. 8m3 - 729 4. 8a3 + 64b3