Question 3(vii)
Simplify:
(a+b+c)(a+b-c)

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Solution

$(a + b + c) (a + b - c) = a (a + b - c) + b (a + b - c) + c (a + b - c)$
$= a^{2} + a b - a c + a b + b^{2} - b c + a c + b c - c^{2}$
$= a^{2} + a b + a b - a c + a c - b c + b c + b^{2} - c^{2}$
$= a^{2} + b^{2} - c^{2} + 2 a b$

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