Question

Find the value of \[{\left( {92} \right)^2} - {\left( {91} \right)^2} = ?\]

Answer 1

Hint:
We can use the algebraic identity \[{a^2} - {b^2} = \left( {a + b} \right)\left( {a - b} \right)\]. Because both the numbers are near to 90 and their difference is only 1. So we will use this identity.

Complete step by step solution:
Here a=92 and b=91.
\[
  {\left( {92} \right)^2} - {\left( {91} \right)^2} = \left( {92 + 91} \right)\left( {92 - 91} \right) \\
   \Rightarrow 183 \times 1 \\
   \Rightarrow 183 \\
\]

Additional information:
There are many algebraic identities in mathematics that makes the calculative part easy.
These satisfy their equation for any value of the variable.
There are some identities that use binomial theorems for their expansion. These are frequently used identities. They are available upto power 4 but we can extend them as we need.
The factoring formulas used are also the algebraic identities. These are used when we need to split a number and then use its expansion.
There exist some three variable identities.

Note:
Don’t go for finding the square and waste your time in this case. Simply use identity.
\[\left( {a - b} \right)\left( {a + b} \right) = {a^2} + ab - ab + {b^2} = {a^2} + {b^2}\]