Diana lost her calculator and is wondering, "Which is larger 2354 or 3245?" She rewrites 32 45 as follows:

Step 1: 32 45 = (23 + 9) (54 9)

Step 2: = 23 54 + 9 54 9 23 81 = 23 54 + 9(54 23) 81

Step 3: = 223 x 54 + 9(54-23) - 81

and she concludes that 23 54 < 32 45.

a. Describe what Diana does in step (1). Your answer should be something like, "Diana rewrote 32 as...and 45 as..."

b. What happens from step (1) to line (2)?

c. What happens from step (2) to line (3)?

d. How does line (3) indicate to Diana, without any further computations, that 32 45 is larger than 23 x 54?