Question

Add a³ + b³ − 3 to the sum of 2a³ − 3b³ − 3ab + 7 and −a³ + b³ + 3ab −9.

Answer 1

First, we need to find the sum of 2a³ - 3b³ - 3ab + 7 and - a³ + b³ + 3ab - 9.
= (2a³ - 3b³ - 3ab + 7) + (- a³ + b³ + 3ab - 9)
Collecting positive and negative like terms together, we get
= 2a³ - a³- 3b³ + b³ - 3ab + 3ab + 7 - 9
= a³ - 2b³ - 2

Now, the required expression = (a³ + b³ - 3) + (a³ - 2b³ - 2).
= a³ + a³ + b³- 2b³ - 3 - 2
= 2a³ - b³ - 5