Use identities to evaluate \[{\left( {97} \right)^2}\] .

Hint:Solve using formula
 \[\left[ {{{\left( {a - b} \right)}^2} = {a^2} + {b^2} - 2ab} \right]\]


Complete step-by-step solution:
\[{\left( {97} \right)^2} = {\left( {100 - 3} \right)^2}\]
By using the formula given in hint
\[\left[ {{{\left( {a - b} \right)}^2} = {a^2} + {b^2} - 2ab} \right]\]
We get,
\[ = {\left( {100} \right)^2} + {\left( 3 \right)^2} - 2\left( {100 \times 3} \right)\]
\[ = {\left( {100} \right)^2} + {\left( 3 \right)^2} - 2\left( {300} \right)\]
\[ = \left( {100 \times 100} \right) + \left( {3 \times 3} \right) - \left( {2 \times 300} \right)\]
\[ = 10000 + 9 - 600\]
\[ = 1009 - 600\]
\[ = 9409\]
Therefore 9409 is the required solution.
An identity is a mathematical equality that connects one mathematical expression A to another mathematical expression B, such that A and B (which may include some variables) generate the same value for all values of the variables within a given range of validity.

Note: A variable and constant expression is known as an algebraic expression. A variable in an expression may have any meaning. As a result, if the variable values change, the expression value will change. Algebraic identity, on the other hand, is equality that holds for all values of the variables.
The substitution approach is used to verify the algebraic identities. Substitute the values for the variables and perform the arithmetic operation with this process. The activity method is another way to check the algebraic identity. You'll need a basic understanding of geometry for this process, as well as some materials to prove your identity.