Question

Evaluate the value of ${(198)^2}$ using the identity${(a - b)^2} = {a^2} - 2ab + {b^2}$.

Answer 1

Hint: Here we go through by writing the term 198 as (200-2) because in the question we have to write in the two terms. So for solving this always think of the two numbers whose square we find easily.

Here we write 198 as (200-2)
And in the question the given identity is ${(a - b)^2} = {a^2} - 2ab + {b^2}$
We have to evaluate our number using this identity.
So we can say (200-2) is the same as (a-b) so we simply put a as 200 and b as 2 in the given identity to evaluate.
By putting the values we get,
${\left( {200 - 2} \right)^2} = {200^2} - 2 \times 200 \times 2 + {2^2}$
Now simplify the term that is on the right hand side,
i.e. R.H.S= ${200^2} - 2 \times 200 \times 2 + {2^2}$
=40000-800+4
=39196
Hence we get the answer by the help of identities that are given in the question.
For cross checking you simply find the square of 198 i.e. $198 \times 198 = 39196$ which also gives the same answer.

Note: Whenever we face such a type of question the key concept for solving the question is always think of the number in that way whose square you easily find. Here in this question the simple way is (200-2) you can also choose different numbers such as (202-4) for the identities, but in this case for finding the square of 202 is little bit complex as finding the square of 200. So always choose a simple number to prove the identities.