5. Obtain the binomial coefficients for (a + b)³ from those for (a + b)² in the style of lines (3*), (4*), (5*) on page 2.

6. Obtain the binomial coefficients for (a + b)⁶ from those for (a + b)⁵ in the style of lines (3*), (4*), (5*) on page 2.

7. Generate the lines of the Pascal Triangle for n = 6 and n = 7, using the technique described immediately below the table on page 3.

8. Find

9. Use

10. Use

11. Expand (5x + 2y)³.

12. Expand (x² - 4y²)³ by letting a = x² and b = -4y² in the expansion of (a + b)³.

13. Show that:

(a) (x - y)⁴ = x⁴ - 4x³y + 6x²y² - 4xy³ + y⁴.

(b) (x - y)⁵ =

14. Show that:

(a) (x + 1)⁶ + (x - 1)⁶ = 

(b) (x + y)⁶ - (x - y)⁶ =

15. Show that (x + h)³ - x³ = h(3x² + 3xh + h²).

16. Show that (x + h)¹⁰⁰ - x¹⁰⁰ =

17. Find numerical values of c and m such that cx³y^m is a term of the expansion of (x + y)⁸.