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# Simplify the Following Using the Identities: $\Frac{{58}^2 - {42}^2}{16}$ - Mathematics

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.

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.6 | Q 5.1 | Page 43
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