Subtracting Polynomials

What expression must be subtracted from 3a - 2b - c to get a difference of 4a - 3b?
A.)  a - b + c
B.)  -a + b - c
C.) 7a - 5b - c
D.)  -7a + 5b + c

Similar to deciding what number must be subtracted from 7 to get a difference of 4, you could subtract 4 from 7 and find out it is 3.

In this one, subtract the difference of (4a - 3b) from (3a - 2b - c)

(3a - 2b - c) - (4a - 3b)   {subtracted}
= 3a - 2b - c - 4a + 3b   {removed parentheses, distributing negative sign}
= -a + b - c   {combined like terms}

B.)  -a + b - c

Proof:
(3a - 2b - c) - (-a + b - c) should equal (4a - 3b)
= 3a - 2b - c + a - b + c   {removed parentheses, distributing negative sign}
= 4a - 3b   {combined like terms}

- Algebra House