Question : Simplify the following expression:
$\frac{\left(a^2+b^2-c^2\right)^2-\left(a^2-b^2+c^2\right)^2}{b^2-c^2}$
Option 1: $3a^2$
Option 2: $4a^2$
Option 3: $5a^2$
Option 4: $2a^2$
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Correct Answer: $4a^2$
Solution :
Given: $\frac{(a^2+b^2-c^2)^2-(a^2-b^2+c^2)^2}{b^2-c^2}$
$= \frac{(a^2+b^2-c^2+a^2-b^2+c^2)(a^2+b^2-c^2-a^2+b^2-c^2)}{b^2-c^2}$
$= \frac{(2a^2)(2b^2-2c^2)}{b^2-c^2}$
$= \frac{4a^2(b^2-c^2)}{b^2-c^2}$
$= 4a^2$
Hence, the correct answer is $4a^2$.
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