Answer in Brief
Simplify the following using the identities: \[\frac{{58}^2 - {42}^2}{16}\]
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Solution
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.
Concept: Concept of Identity
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