Question

How do you simplify $18{x^2} + 4 - [6\left( {{x^2} - 2} \right) + 5]$?

Answer 1

Hint: We are given an algebraic expression and we have to simplify it to simplify an algebraic expression. We will use the rule of BODMAS. Here BODMAS stands for B- bracket, O- of, D- divide, M- multiplication, A- addition, S- Subtraction. First we solve the bracket in which a number is multiplied with the small bracket. So we will remove parenthesis by removing the small bracket then we will rearrange and add the like terms then we will open the big bracket with the negative sign after opening with the negative sign the sign will get reversed. Then we will rearrange the terms then add or subtract the like comes together then factor out the common digit from them.

Complete step-by-step answer:
Step1: We are given an algebraic expression $18{x^2} + 4 - [6\left( {{x^2} - 2} \right) + 5]$ then we will use the rule of BODMAS for it. Here BODMAS stands for B- bracket, O- of, D- divide, M- multiplication, A- addition, S- Subtraction. Here first we will solve the big bracket part in that we will first multiply $6$ to the entire bracket to remove parenthesis then we get:
$ \Rightarrow 18{x^2} + 4 - [6{x^2} - 12 + 5]$
Then we subtract 5 from 12 we get:
$ \Rightarrow 18{x^2} + 4 - \left[ {6{x^2} - 7} \right]$
Step2: Now we will open the bracket with the multiplication sign.
$ \Rightarrow 18{x^2} + 4 - 6{x^2} + 7$
Then we will arrange the like terms together:
$ \Rightarrow 18{x^2} - 6{x^2} + 4 + 7$
Now we will subtract $6{x^2}$ from $18{x^2}$ and add 4 and 7:
$ \Rightarrow 12{x^2} + 11$

Step3: Final answer: Hence the simplified form is $12{x^2} + 11$

Note:
In this type of question students sometimes don't follow the rule of BODMAS. But the correct way of solving this question is to use this rule and students sometimes also make mistakes in multiplying the negative sign while opening the bracket. So just kept in mind whenever a minus sign is multiplied then sign gets reversed in case of Plus sign no changes take place.