Question

Find the excess of \[4(a - b - c)\] over \[3(a + b)\] and subtract \[9(a - 2b + bc)\] from the result. The final answer will be
a. \[( - 8a + 11b - 4c - 9bc)\]
b. \[(8a + 11b - 4c - 9bc)\]
c. \[( - 8a - 11b - 4c - 9bc)\]
d. \[( - 8a - 11b + 4c - 9bc)\]

Answer 1

Hint: In the first step, we subtract \[3(a + b)\] from \[4(a - b - c)\], and then subtract \[9(a - 2b + bc)\] from the result we get, to get the final result.

Complete step by step answer:

Initially we are given the task to find the excess of \[4(a - b - c)\] over \[3(a + b)\]. So, for that we will have to subtract \[3(a + b)\] from \[4(a - b - c)\],
So by subtracting we get,
\[
  4(a - b - c) - 3(a + b) \\
   = 4a - 4b - 4c - 3a - 3b \\
   = a - 7b - 4c \\
 \]
Now from the result we have to subtract \[9(a - 2b + bc)\],
Then we have,
\[
  (a - 7b - 4c) - 9(a - 2b + bc) \\
   = a - 7b - 4c - 9a + 18b - 9bc \\
   = - 8a + 11b - 4c - 9bc \\
 \]
So, we have the answer as, \[ - 8a + 11b - 4c - 9bc\] which is option (a).

Note: If we talk about the excess term here, it is a bit confusing to deal with. The excess over a term means how much bigger the first term is than the 2nd term here. So, we need to take care of that a bit to get the correct answer.