1. Same Sign Opposite Sign Always Positive
Just as there is a special rule for factoring the difference of two squares, there are special rules for factoring the sum or difference of two cubes.
=( 3 1𝑠𝑡 S 3 2𝑛𝑑 ) ( 𝑠𝑡 2 O 3 1𝑠𝑡 ∗ 3 2𝑛𝑑 AP 𝑛𝑑 2 )
Same Sign
Opposite Sign
Always Positive

2. Example 3A: Factoring the Sum or Difference of Two Cubes
Factor the expression.
4x x
4x(x3 + 27)
Factor out the GCF, 4x.
4x( )( – ) x 3 x2 3x 9

3. Example 3B: Factoring the Sum or Difference of Two Cubes
Factor the expression.
125d3 – 8
( – )( ) 5d 2
25d2
10d 4

4. 8 + z6 ( + )( – + ) 2 z2 4 2z2 z4 Check It Out! Example 3a
Factor the expression.
8 + z6
( )( – ) 2 z2 4
2z2 z4

5. 216c6 – 343 d12 ( – )( + + ) 6c2 7d4 36c4 42c2d4 49d8 Challenge
Factor the expression.
216c6 – 343 d12
( – )( )
6c2
7d4
36c4
42c2d4
49d8