Question

If the value of a = 2 and the value of b = -2, then what will be the value of ${a^2} - {b^2}$ ?

Answer 1

Hint: we will just use the approach that we will just expand the given expression that we have to evaluate by using the simple algebra identity that ${a^2} - {b^2} = (a + b)(a - b)$ and then substitute the value of a and b so given in the expression to get the required value.

Complete step-by-step answer:
It is given that we have to find the value of expression ${a^2} - {b^2}$
Using the identity ${a^2} - {b^2} = (a + b)(a - b)$
Now, we have been given that the value of a = 2 and the value of b = -2.
We will just substitute the values in the following expression to get the required answer.
$ = (2 + ( - 2))(2 - ( - 2))$
We know that in the algebra, $ + ( - a) = - a, - ( - a) = a$
$ = (2 - 2)(2 + 2)$
$ = 0 \times 4$
$ = 0$
Thus, the expression evaluates down to 0.
Hence, the required value of the expression ${a^2} - {b^2}$ when the value of a = 2 and the value of b = -2 is 0.

Note- In such types of questions, we can just simplify the expression using another method by simply substituting the value of a and b in the expression and by using the power of a function concept we can also evaluate the expression like ${a^2} - {b^2}$ on substituting the value of a =2 and b = -2 becomes ${(2)^2} - {( - 2)^2}$ which evaluates down to $4 - 4$ which is equal to 0. That’s another direct method of solving without using identity.