Question

Subtract $24ab - 10b - 18a$ from $30ab + 12b + 14a$

Answer 1

Hint:
Here, we are required to subtract one algebraic expression from the other. We will subtract the first equation from the second equation by converting the sign of the first equation. Then we will apply the desired mathematical operation to terms with the same variables to get the required answer.

Complete step by step solution:
In order to subtract one algebraic expression from the other,
First of all, we will write the like terms below each other and then, since we are required to do subtraction, thus, we will write the opposite sign i.e. if there is a negative sign then we will interchange it with a plus sign and vice-versa.
Hence, this can be written as:
Difference $ = 30ab + 12b + 14a - \left( {24ab - 10b - 18a} \right)$
Now multiplying negative sign to the terms in the bracket, we get
$ \Rightarrow $ Difference $ = 30ab - 12b + 14a - 24ab + 10b + 18a$
Adding and subtracting the like terms, we get
$ \Rightarrow $ Difference $ = 6ab + 22b + 32a$
Now taking 2 common, we get
$ \Rightarrow $ Difference $ = 2\left( {3ab + 11b + 16a} \right)$

Therefore, when we subtract $24ab - 10b - 18a$ from $30ab + 12b + 14a$, we get, $6ab + 22b + 32a$ or $2\left( {3ab + 11b + 16a} \right)$.
Thus, this is the required answer.

Note:
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations. Since, in this question, we were required to subtract one algebraic expression from the other, so we need to take care of the signs. Here we have changed the sign of first expression because when $\left( - \right)$ is multiplied to $\left( + \right)$ it gives $\left( - \right)$ sign but when $\left( - \right)$ is multiplied to $\left( - \right)$ sign it gives $\left( + \right)$. Also, it is really important to subtract the terms from the preceding terms having the same variables. If the variable of all the terms are different then we cannot add or subtract the terms.