Mark the correct alternative in each of the following:

Using cosine rule, we have

$a(b \cos C-c \cos B)$

$=a b\left(\frac{a^{2}+b^{2}-c^{2}}{2 a b}\right)-c a\left(\frac{c^{2}+a^{2}-b^{2}}{2 c a}\right)$

$=\frac{a^{2}+b^{2}-c^{2}-c^{2}-a^{2}+b^{2}}{2}$

$=\frac{2 b^{2}-2 c^{2}}{2}$

$=b^{2}-c^{2}$

Hence, the correct answer is option (b).