Answer
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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.
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.
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