Question

How do you simplify:
 \[
  A = \left( {8 - b} \right)\left( { - 3} \right) + 6b + 12 - 10b \\
    \\
\]

Answer 1

Hint: The given algebraic expression can be evaluated by first solving the brackets and then adding up the instances of the variables \[b\] and then rearranging them. We would also keep in mind that variable (for example: \[x,y,z,a,b,c\] ) are not added with constants (for example numbers ie \[1,2,3,4,\] etc ) they are kept as separate terms in the algebraic expression.

Complete step-by-step answer:
We are given the algebraic expression,
 \[\left( {8 - b} \right)\left( { - 3} \right) + 6b + 12 - 10b\] ,
Let the expression be \[A\] then we can write,
 \[A = \left( {8 - b} \right)\left( { - 3} \right) + 6b + 12 - 10b\]
We will now solve the first term of expression \[A\] which is \[\left( {8 - b} \right)\left( { - 3} \right)\]
 \[A = [8*( - 3) - \{ b*( - 3)\} ] + 6b + 12 - 10b\]
Upon further solving the expression we get,
 \[A = [ - 24 - ( - 3b)] + 6b + 12 - 10b\]
Which can be solved as,
 \[A = [3b - 24] + 6b + 12 - 10b\]
Now we open the bracket and write variable part and constant part of the expression next to each other,
 \[A = 3b + 6b - 10b + 12 - 24\]
Now we add all the terms containing the variable which is \[b\] and add all the constant terms
 \[A = - b - 12\]
Which can be rearranged and written as follows:
 \[A = - (b + 12)\]
Which is our desired answer
So, the correct answer is “ \[A = - (b + 12)\] ”.

Note: Algebraic expressions are the mathematical expressions that are composed of both variables like \[x,y,z,a,b,c\] and constants like \[1,2,3,25,\] etc. The variables and constants can be added to each other like we do with numbers they rather are added only to the parts of the expression which has the same variable with same exponential power on them so we should understand that \[x + 2x = 3x\] but \[2{x^2} + x \ne 3{x^2}\] because one of the
 \[x\] does not have the same powers as the other \[x\] which have the power \[2\] . This should not be confused with the fact that constant and variable can easily be multiplied but they keep expressing themselves as well for example: \[2*x = 2x\]