Question

If z=10, find the value of ${{z}^{3}}-3(z-10)$.

Answer 1

Hint: To solve this problem, we must be aware about the basic arithmetic (in this case addition) operations along with application of the BODMAS rule. In this problem, we simply substitute the value of z in the expression and then evaluate the expression.

Complete Step-by-step answer:
Before we begin the problem, we try to understand the basics of BODMAS rule. BODMAS is an acronym and it stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. It explains the order of operations to solve an expression. According to BODMAS rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots), then division, multiplication, addition and subtraction from left to right. Solving the problem in the wrong order will result in a wrong answer. Thus, to explain, we take an example. Suppose, we have to evaluate-
3 + 4 $\times $ 5 $\times $ (6-2)
According to BODMAS rule, we first start with brackets (that is 6-2 = 4). Thus, we get,
3 + 4 $\times $ 5 $\times $ (4)
Now, we carry the multiplication operations (that is, 4$\times $5$\times $4= 60), thus, we get,
3 + 80 = 83
Now, we use similar principles to solve the above problem, we have,
${{z}^{3}}-3(z-10)$
Substituting z = 10,
=${{10}^{3}}-3(10-10)$
First, bracket operations are evaluated, thus,
$\begin{align}
  & ={{10}^{3}}-3(0) \\
 & ={{10}^{3}} \\
\end{align}$
= 1000
Hence, the value of the above expression is 1000.

Note: While solving the questions involving arithmetic operations, it is important to solve in proper order. For example, we know that 3 + 4 $\times $ 5 $\times $ (6-2) = 83. However, if we evaluated 3 + 4 = 7 first, we would have got 7 $\times $ 5 $\times $ 4 = 140 (which is incorrect). Thus, it is important to follow the correct order.