What is the value of $\left( {7.5 \times 7.5 + 37.5 + 2.5 \times 2.5} \right)$?
A). $30$
B). $60$
C). $80$
D). $100$

Hint: In the given problem we have to find the value of the numbers. We can use the basic arithmetic operations to solve the problem. It is a basic simplification problem. We can solve this problem in two methods. One method is basic simplification using arithmetic operations and the second method is using algebraic formulas.
Formula used:
 In the given problem we used the formulae given below.
${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$

Complete step-by-step solution:
In the given problem we are going to find the value of the numbers.
First, we solve the problem using the formula.
The given term is $7.5 \times 7.5 + 37.5 + 2.5 \times 2.5$
We can write this as, ${\left( {7.5} \right)^2} + 2 \times 7.5 \times 2.5 + {\left( {2.5} \right)^2}$
Now compare the above term to the formula ${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$
Here,
 $
  a = 7.5 \\
  b = 2.5 \\
  2ab = 2 \times 7.5 \times 2.5 $
Therefore now apply the formula on the term we get,
$7.5 \times 7.5 + 37.5 + 2.5 \times 2.5 = {\left( {7.5 + 2.5} \right)^2}$
Now simplify the term, ${\left( {7.5 + 2.5} \right)^2}$
Now we get, ${\left( {7.5 + 2.5} \right)^2} = {\left( {10} \right)^2}$
Therefore ten squares are equal to a hundred.
${\left( {7.5 + 2.5} \right)^2} = \left( {10 \times 10} \right)$
Therefore now we get,
${\left( {7.5 + 2.5} \right)^2} = \left( {100} \right)$
Therefore the answer to the given question is a hundred.
We solved the problem using the formula method.
With another method, we can solve this problem using arithmetic functions.
That is the given term is, \[7.5 \times 7.5 + 37.5 + 2.5 \times 2.5\]
Now we use the BODMAS rule to solve this.
We can write the term as,
\[\left( {7.5 \times 7.5} \right) + 37.5 + \left( {2.5 \times 2.5} \right)\]
By the BODMAS rule first, we have to solve the brackets.
So multiply the terms inside the brackets.
We get, \[56.25 + 37.5 + 6.25\]
Now apply the addition operation, we get
\[56.25 + 37.5 + 6.25 = 100\]
Hence we get the solution is a hundred.
Therefore the value of the given term is a hundred.
Hence the solution for the given question is option D.

Note: We used the BODMAS rule to solve the problem. By the BODMAS rule, we can solve the Brackets first, next the Orders. After that, we can solve the Division. After that, we can solve the Multiplication. After solving the multiplication we go-to addition. At last, we do the subtraction. This is called the rule of BODMAS.