Question

Using identities, evaluate the following: \[{97^2}\] ?

Answer 1

Hint: The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. We should take care about splitting this value. our splitting value should be in round of \[10\] , \[100\] etc or easy to calculate values.
Not like that \[97 = 95 + 2\] .

Complete step-by-step answer:
To solve these types of questions, we should try to split the given value in some form of addition or subtraction and try to make them in the form of identities.
We are splitting 97 in terms of 100 and 3 because squaring of 100 is easy
 \[97 = 100 - 3\]
Now, using the formula \[\]
 \[{\left( {a-b} \right)^2} = {a^2}-2ab + {b^2}\]
 \[{97^2} = {(100 - 3)^2}\]
Now, we will expand our R.H.S using the formula \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]
 \[{97^2} = {100^2} + {3^2} - 2 \times 100 \times 3\]
 \[ = 10000 + 9 - 600\]
 \[ = 9409\]
So, using the identity square of 97 is 9409.
So, the correct answer is “ 9409”.

Note: The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials. An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. Thus, the expression value can change if the variable values are changed. But algebraic identity is equality which is true for all the values of the variables.