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