Subtract the number $4 a − 7 a b + 3 b + 12$ from $12 a − 9 a b + 5 b − 3$ . Then

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− 8 a − 16 a b + 2 b − 15

8 a − 2 a b + 2 b − 15

16 a − 2 a b + 2 b − 9

None of these

answer is B.

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Detailed Solution

We are given that the two numbers to be subtracted as

4 a − 7 a b + 3 b + 12

and

12 a − 9 a b + 5 b − 3

.
Let us assume that the first number as
⇒ P = 4a − 7ab + 3b + 12
Similarly, let us assume that the second number as
⇒ Q = 12a − 9ab + 5b – 3
We are asked to subtract the number

4 a − 7 a b + 3 b + 12

from

12 a − 9 a b + 5 b − 3

The above statement can be modified as to subtract P from Q
Let us assume that the result in the above subtraction as R
We know that the condition that subtraction of x from y is given as y − x
By using the above result to given numbers we get
⇒ R = Q − P
By substituting the required values in above equation we get
⇒ R = (12a − 9ab + 5b − 3) − (4a − 7ab + 3b + 12)
We know that we need to add or subtract the terms with the same variable.
So, let us rearrange the terms in the above equation such that we get the terms of same variable as a group then we get
⇒R = (12a − 4a) + (− 9ab + 7ab) + (5b − 3b) + (− 3 − 12)
⇒R = 8a − 2ab + 2b – 15
Therefore we can conclude that the result after subtracting 4a − 7ab + 3b + 12 from
12a − 9ab + 5b − 3 is given as 8a − 2ab + 2b − 15.

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