Special Rules.

20. $(x^{2}y+x{y}^2)(x^{2}y+x{y}^2)$.

21. $(x+a)(x+b)$.

22. $(x+a)(x-b)$.

23. $(x-a)(x+b)$.

24. $(x-a)(x-b)$.

25. $(x+2a)(x+2b)$.

26. $(x-2a)(x+2b)$.

27. $(x+2a)(x-2b)$.

28. $(x-2a)(x-2b)$.

29. $(x-a)(x+3a)$.

30. $(x-2a)(x+3a)$.

98. Special Rules of Division.

Some results in division are so important in abridging algebraic work that they should be carefully noticed and remembered.

99. Difference of Two Squares.

Since $(a+b)(a-b)=a^2-b^2$, $\therefore \frac{a^2-b^2}{a+b}=a-b;\text{and}\frac{a^2-b^2}{a-b}=a+b.\text{quadtext{Hence,}\}$

The difference of the squares of two numbers is divisible by the sum, and by the difference, of the numbers.

Exercise 28.

Write by inspection the quotient of:

1. ${\displaystyle \frac{x^2-4}{x-2}}$.

2. ${\displaystyle \frac{x^2-4}{x+2}}$.

3. ${\displaystyle \frac{a^2-9}{a-3}}$.

4. ${\displaystyle \frac{a^2-9}{a+3}}$.

5. ${\displaystyle \frac{c^2-25}{c-5}}$.