Example 1. Expand (2x + 3y²)³.

Solution: The expansion (a + b)³ = a³ + 3a²b + 3ab² + b³ is an identity which remains true when one substitutes a = 2x and b = 3y² and thus obtains

         (2x + 3y2)3 = (2x)3 + 3(2x)2(3y2) + 3(2x)(3y2)2 + (3y2)3
                    = 8x3 + 3(4x2)(3y2) + 3(2x)(9y4) + 27y6
                    = 8x3 + 36x2y2 + 54xy4 + 27y6.

Example 2. Show that

Solution: Using the fact thatand the formula we see that

Problems for Chapter 1

1. Give the value of that is, of the coefficient of a³b² in (a + b)⁵.

2. Give the value of 

3. Find s ifand s is not 4.

4. Find t ifand t is not 0.