Question

Evaluate the value \[\left( 9.8 \right)^{2}\] by using the identity \[\left( a - b \right)^{2} = a^{2} + b^{2} - 2ab\]

Answer 1

Hint: In this question, we need to evaluate \[\left( 9.8 \right)^{2}\]. And also given that we need to evaluate by using the identity \[\left( a – b \right)^{2} = a^{2} + b^{2} – 2ab\] . First we need rewrite the given \[\left( 9.8 \right)^{2}\] in the terms of \[\left( a – b \right)^{2}\] .Then by simplifying we get the value of \[\left( 9.8 \right)^{2}\].

Complete step-by-step solution:
Given,
\[\left( 9.8 \right)^{2}\]
Using the identity \[\left( a – b \right)^{2} = a^{2} + b^{2} – 2ab\] we need to evaluate \[\left( 9.8 \right)^{2}\]
Now we can write \[\left( 9.8 \right)^{2}\] as \[\left( 10 – 0.2 \right)^{2}\]
Now we can expand \[\left( 10 – 0.2 \right)^{2}\]
\[\ \left( 10 – 0.2 \right)^{2} = \left( 10 \right)^{2} + \left( 0.2 \right)^{2} – 2\left( 10 \right)\left( 0.2 \right)\]
By simplifying,
We get,
\[\left( 10 – 0.2 \right)^{2} = 100 + 0.04 – 4\]
On further simplifying,
We get,
\[\left( 10 – 0.2 \right)^{2} = 96.04\]
Thus \[\left( 9.8\right)^{2} = 96.04\]
Final answer :
The value of \[\left( 9.8\right)^{2} = 96.04\].
Additional information :
Basically it can also be solved by simply squaring the given term without using the identity. In this question, they mentioned that we need to use the identity, so we have expanded with using the identity. Mathematically, the square numbers are non – negative . The square of the integer is also known as the square number or a perfect square. For example \[3^{2} = 9\] is the perfect square . Every non-negative real number is a square number. Mathematically, squaring is used in statistics, probability, etc… In other words, all the non negative integers are square numbers.


Note: The concept used to solve this problem is algebraic identities. Algebraic Identities are used for the Factorization of the polynomials. There are eight more algebraic identities used for the factorization of the polynomial. Expanding algebraic expression is nothing but combining one or more variables or numbers by performing the given algebraic operations.