The value of (107) $^{2}$ - (93) $^{2}$ is: ____.

2800

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1008

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1382

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36482

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Solution

The correct option is A 2800
(107) $^{2}$ can be written as (100+7) $^{2}$ and (93) $^{2}$ can be written as (100-7) $^{2}$ .
$107^{2} - 93^{2} = (100 + 7)^{2} - (100 - 7)^{2}$ .
This is in the form of $(a + b)^{2} - (a - b)^{2}$ where a = 100 and b=7

We know that, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ and $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$(a + b)^{2} - (a - b)^{2} = a^{2} + 2 a b + b^{2} - a^{2} - 2 a b + b^{2} = 4 a b$
$107^{2} - 93^{2} = 4 a b = 4 \times 100 \times 7 = 2800$

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