Question

How do you simplify \[\left[ \left( 8+5 \right){{\left( 6-2 \right)}^{2}} \right]-\dfrac{4x17}{2}\] ?

Answer 1

Hint: This particular given problem includes some of the basic and advanced concepts like factorisation, linear equations and the law of associativity. Applying these things along with simple addition and multiplication we will be able to solve the given problem very easily. For this particular problem, we first need to solve everything which is inside of the bracket and evaluate them. Having done this, we will then subtract the left-hand term from it, which will give us our desired answer. We have to consider the unknown parameter in this equation separately and not mix it with the other general constant terms.

Complete step by step solution:
Now we start off with the solution to the problem by writing that,
First of all we add and subtract the required terms present inside of the bracket and then proceed. We get,
\[\Rightarrow \left[ 13{{\left( 4 \right)}^{2}} \right]-\dfrac{4x17}{2}\]
Multiplying the terms we get,
\[\Rightarrow 208-\dfrac{4x17}{2}\]
Now, we divide the numerator and the denominator of the right hand term by 2, and we get,
\[\Rightarrow 208-34x\]
We cannot proceed further because we cannot further subtract as they are not like terms. So \[208-34x\] will be our required answer.

Note: For such types of problems, we first of all need to keep in mind the different concepts that are included in linear equations, factor theorem and the various laws including the laws of associativity and distributive property. We must also be very careful while handling the unknown parameters and not perform simple math operations with the other constant terms. We need to remember that we can do math operations on like terms only.