-a-b-c-a-b-c- - -nbsp-a-2 - b-2 - c-2 - bc-a-2 - b-2 nbsp- c-2 - ca-a-2 - b-2 - c-2 - 2ca-a-2 - b-2 nbsp- c-2 - 2bc-

The correct option is D a^2 b^2 nbsp; c^2 2bc (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 ...

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Multiplication of a Monomial and a Polynomial

(a+b+c)(a-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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If a + b + c = 2s, then prove the following identities

(a) s² + (s − a)² + (s − b)² + (s − c)² = a² + b² + c²

(b) a² + b² − c² + 2ab = 4s (s − c)

(d) a² − b² − c² + 2ab = 4(s − b) (s − c)

(e) (2bc + a² − b² − c²) (2bc − a² + b² + c²) = 16s (s − a) (s − b) (s − c)

(f)

Factorise by taking out the common factors:

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

|\begin{matrix} - a (b^{2} + c^{2} - a^{2}) & 2 b^{3} & 2 c^{3} \\ 2 a^{3} & - b (c^{2} + a^{2} - b^{2}) & 2 c^{3} \\ 2 a^{3} & 2 b^{3} & - c (a^{2} + b^{2} - c^{2}) \end{matrix}| = a b c {(a^{2} + b^{2} + c^{2})}^{3}

If a, b, c, d are in G.p., prove that :

(i) $(a^{2} + b^{2}), (b^{2} + c^{2}), (c^{2} + d)^{2}$ are in G.P.

(ii) $(a^{2} - b^{2}), (b^{2} - c^{2}), (c^{2} - d)^{2}$ are in G.P.

(iii) $\frac{1}{a^{2} + b^{2}}, \frac{1}{b^{2} + c^{2}}, \frac{1}{c^{2} + d^{2}}$ are in G.P.

(iv) $(a^{2} + b^{2} + c^{2}), (a b + b c + c d), (b^{2} + c^{2} + d^{2})$

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

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

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