How much is 21a3 - 17a2 less than 89a3 - 64a2 + 6a + 16?

To find how much one polynomial is less than another, subtract the smaller from the larger and simplify by combining like-degree terms; any term missing from the polynomial being subtracted carries over unchanged.

1. Set up the subtraction: (89a3 - 64a2 + 6a + 16) - (21a3 - 17a2).

2. Distribute the negative sign across the second polynomial: 89a3 - 64a2 + 6a + 16 - 21a3 + 17a2.

3. Group terms of the same degree: (89 - 21)a3 + (-64 + 17)a2 + 6a + 16.

4. Simplify each group to get the result: 68a3 - 47a2 + 6a + 16.

Check by adding the result back to the subtracted polynomial: (68a3 - 47a2 + 6a + 16) + (21a3 - 17a2) = 89a3 - 64a2 + 6a + 16, which reproduces the original larger polynomial.