(a+b+c)(a+b c)=a^2+ab ac+ba+b^2 bc+ca+cb c^2 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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(x + a)(x +b)= x^2 + x(a+ b) + ab

Simplify: a...

Question

Simplify: $(a + b + c) (a + b - c)$

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Solution

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

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

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

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

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