Question

Subtract \[a(b - 5)\] from \[b(5 - a)\].

Answer 1

Hint: This is a simple question of subtraction of variables. We first simplify our bracket first according to the BODMAS rule and then subtract our numbers.
We will subtract the coefficient of those variables which are of the same type and use the sign of greater number in our answer.

Complete step by step solution: Whenever it is given that subtract A from B then we write it as B – A not A – B.
So start solving simplify our bracket first,
i.e. \[a(b - 5) = ab - 5a\]
and \[b(5 - a) = 5b - ba\][ but\[ab = ba\]]
Hence \[b(5 - a) = 5b - ab\]
Now we subtract our both equations
i.e. \[5b - ab - (ab - 5a)\]
If we have a negative sign outside the bracket then the inner sign will change when we remove it i.e. plus sign will become minus sign and also minus sign will become plus sign. If no sign is marked with a number it is considered as a positive number.
\[5b{\text{ }}-{\text{ }}ab{\text{ }}-{\text{ }}ab{\text{ }} + {\text{ }}5a\]………….(1)
Here we can solve only variables of the same types. For example x can be added or subtracted from x only not from y or \[{x^2}\].
So\[-{\text{ }}ab\] and \[-{\text{ }}ab\] are of the same type of variable and if both numbers are negative we will perform addition but the sign will be negative here.
Therefore \[-{\text{ }}ab{\text{ }}-{\text{ }}ab = - 2ab\]
So equation (1) will become \[5b - 2ab + 5a\]
Or you can also write it as \[5a + 5b - 2ab\].

Note: Dear students, always take care of signs while solving these types of questions. Any single mistake of sign will lead to the wrong answer. Also remember variables of the same type only can be added or subtracted. Variables and their power must be the same. If not, they will remain as it is.