Question
Simplify the following using the identities:
$\frac{58^2−42^2}{16}$
$\frac{58^2−42^2}{16}$
✓
Answer
Let us consider the following expression:
Using the identity $(a+b)(a-b)=a^2-b^2$
We get:
$\frac{58^2−42^2}{16}$
$\frac{58^2−42^2}{16}=\frac{(58+42)(58−42)}{16}$
$⇒\frac{58^2−42^2}{16}=\frac{100×16}{16}$
$⇒\frac{58^2−42^2}{16}=100$
Thus, the answer is 100.
Using the identity $(a+b)(a-b)=a^2-b^2$
We get:
$\frac{58^2−42^2}{16}$
$\frac{58^2−42^2}{16}=\frac{(58+42)(58−42)}{16}$
$⇒\frac{58^2−42^2}{16}=\frac{100×16}{16}$
$⇒\frac{58^2−42^2}{16}=100$
Thus, the answer is 100.
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