Question:
Divide:
(a2 + 2ab + b2) − (a2 + 2ac + c2) by 2a + b + c
Solution:
$\frac{\left(a^{2}+2 a b+b^{2}\right)-\left(a^{2}+2 a c+c^{2}\right)}{(2 a+b+c)}$
$=\frac{(a+b)^{2}-(a+c)^{2}}{(2 a+b+c)}$
$=\frac{(a+b+a+c)(a+b-a-c)}{(2 a+b+c)}$
$=\frac{(2 a+b+c)(b-c)}{(2 a+b+c)}$
$=b-c$
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