The document discusses the formulas for summing and subtracting cubes. It presents the SOAP rule - Sum Of APs, for expanding and factorizing expressions involving sums and differences of cubes. Some examples are given to demonstrate applying the rule, such as expanding y + 8a and factorizing s - st.

1. Sum and Difference of 2 Cubes

2. Sum and Difference of 2 Cubes
a + b = (a + b)(a − ab + b )
3 3 2 2
a − b = (a − b)(a + ab + b )
3 3 2 2

3. Sum and Difference of 2 Cubes
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
a − b = (a − b)(a + ab + b )
3 3 2 2

4. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2

5. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a =
3 3

6. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a = y + (2a)
3 3 3 3

7. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a = y + (2a)
3 3 3 3
= (y + 2a)(y − 2ay + 4a )
2 2

8. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a = y + (2a)
3 3 3 3
= (y + 2a)(y − 2ay + 4a )
2 2
2. s − st =
4 3

9. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a = y + (2a)
3 3 3 3
= (y + 2a)(y − 2ay + 4a )
2 2
2. s − st = s(s − t )
4 3 3 3

10. Sum and Difference of 2 Cubes
S O AP
Remember the SOAP rule
a + b = (a + b)(a − ab + b )
3 3 2 2
S O AP
a − b = (a − b)(a + ab + b )
3 3 2 2
Examples
1. y + 8a = y + (2a)
3 3 3 3
= (y + 2a)(y − 2ay + 4a )
2 2
2. s − st = s(s − t )
4 3 3 3
= s(s − t)(s + st + t )
2 2