Special Rules.

24. ${\displaystyle \frac{(a+2b{)}^2-4c^2}{(a+2b)-2c}}$.

25. ${\displaystyle \frac{(a+2b{)}^2-4c^2}{(a+2b)+2c}}$.

26. ${\displaystyle \frac{1-(3x-2y{)}^2}{1+(3x-2y)}}$.

100. Difference of Two Cubes.

By performing the division we have $\frac{a^3-b^3}{a-b}=a^2+ab+b^2.\text{quadtext{Hence,}\}$

The difference of the cubes of two numbers is divisible by the difference of the numbers, and the quotient is the sum of the squares of the numbers plus their product.

Exercise 29.

Write by inspection the quotient of:

1. ${\displaystyle \frac{1-x^3}{1-x}}$.

2. ${\displaystyle \frac{1-8a^3}{1-2a}}$.

3. ${\displaystyle \frac{1-27c^3}{1-2c}}$.

4. ${\displaystyle \frac{8a^3-b^3}{2a-b}}$.

5. ${\displaystyle \frac{64b^3-27c^3}{4b-3c}}$.

6. ${\displaystyle \frac{27x^3-8y^3}{3x-2y}}$.

7. ${\displaystyle \frac{x^3{y}^3-z^3}{xy-z}}$.

8. ${\displaystyle \frac{a^3{b}^3-8}{ab-2}}$.

9. ${\displaystyle \frac{125a^3-b^3}{5a-b}}$.

10. ${\displaystyle \frac{a^3-8b^3}{a-2b}}$.

11. ${\displaystyle \frac{a^3-64}{a-4}}$.