Question

Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$.
A.$8a + 2ab + 2b + 15$
B.$8a + 2b + 15$
C.$8a - 2ab + 2b + 15$
D.$8a - 2ab + 2b - 15$

Answer 1

Hint: The problem is given in the form of algebraic expression. An algebraic expression is an expression which is made up of variables and constants. Here, we are given two algebraic expressions and we need to subtract them i.e., we have to subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$. First, we will change the signs of the expression which we need to subtract. After changing the signs we place the like terms together to make the calculation easier. Like terms are the terms that have the same variables and powers and unlike terms are those terms whose variables and powers are different from each other. The coefficients do not need to match. For example, $8y$ and $25y$ are like terms whereas $8x$ and $25y$are unlike terms because their variables are different.

Complete step by step solution:
Given: Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$
Here, we need to Subtract $4a - 7ab + 3b + 12$ from $12a - 9ab + 5b - 3$ so we will change the signs of $4a - 7ab + 3b + 12$ i.e., change positive signs to negative signs and vice versa.
$ \Rightarrow 12a - 9ab + 5b - 3 - \left( {4a - 7ab + 3b + 12} \right)$
Open the bracket
$ \Rightarrow 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12$
Now, place the like terms together
$ \Rightarrow 12a - 4a - 9ab + 7ab + 5b - 3b - 3 - 12$
After solving it, we get
$ \Rightarrow 8a - 2ab + 2b - 15$
Therefore, the correct option is D.
So, the correct answer is “Option D”.

Note: Here, we have changed the signs (positive sign to negative sign and vice versa) of an algebraic expression which we had to subtract from another algebraic expression because here we are subtracting two algebraic expressions. Don’t repeat this step in addition to algebraic expressions. Arrange the like terms together to make the calculations easier. Take care of the signs while subtracting or adding the expressions. Check the calculations.