Question

Simplify the following using the identities: \[\frac{{58}^2 - {42}^2}{16}\]

Answer 1

 Let us consider the following expression: \[\frac{{58}^2 - {42}^2}{16}\]

Using the identity

\[\left( a + b \right)\left( a - b \right) = a^2 - b^2\], we get:

\[\frac{{58}^2 - {42}^2}{16} = \frac{\left( 58 + 42 \right)\left( 58 - 42 \right)}{16}\]

\[\Rightarrow \frac{{58}^2 - {42}^2}{16} = \frac{100 \times 16}{16}\]

\[ \Rightarrow \frac{{58}^2 - {42}^2}{16} = 100\]

Thus, the answer is 100.