(a+b+c)(a b c) =a(a b c)+b(a b c)+c(a b c) =a^2 ab ac + ba b^2 nbsp; bc + ca cb c^2 = (a^2 b^2 nbsp; c^2 2bc) nbsp; ( ∵ ac=ca, bc=cb an ...

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Multiplication of Polynomials

a+b+ca-b-c =

Question

$(a + b + c) (a - b - c)$ = ______

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

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

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

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

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Solution

The correct option is D
$a^{2} - b^{2} - c^{2} - 2 b c$

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

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

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