Question

The value of \[{\left( {101} \right)^2}\] is
A. 103001
B. 10201
C. 10301
D. 102001

Answer 1

Hint: In this question, use an identity to split the terms which we quite often used in the algebra like \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\] for simple calculations. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:

The given number is \[{\left( {101} \right)^2}\]
Now this can be rewrite as \[{\left( {101} \right)^2} = {\left( {100 + 1} \right)^2}\]
Using the formula \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\], we have
\[
  {\left( {101} \right)^2} = {\left( {100} \right)^2} + 2\left( {100} \right)\left( 1 \right) + {\left( 1 \right)^2} \\
  {\left( {101} \right)^2} = 100 \times 100 + 2 \times 100 \times 1 + 1 \times 1 \\
  {\left( {101} \right)^2} = 10000 + 200 + 1 \\
  \therefore {\left( {101} \right)^2} = 10201 \\
\]
Thus, the correct option is A. 10201

Note: If the number in the square is less than 100 , then we use this identity \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]. This method is also called as evaluation of values by using suitable identities.