Discussion
\(\dfrac{(a - b + c)^{2} - (a - b - c)^{2}}{b - a}\) is equal to :
Answer: C
The expression equals \(-4c\).
Use \(X^2 - Y^2 = (X + Y)(X - Y)\) with \(X = a - b + c\) and \(Y = a - b - c\):
\[ \begin{aligned} X + Y &= 2(a - b), \quad X - Y = 2c \\ X^2 - Y^2 &= 4c(a - b) \\ \frac{4c(a - b)}{b - a} &= -4c \end{aligned} \]
The sign comes from \(b - a = -(a - b)\); dropping it gives 4c, which is not offered, and 2c halves the result.
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