-a-b-c-a-b-c- -a2-2ab-c2-a2-2ab-b2-a2-4ab-b2-c2-a2-2ab-b2-c2-

The correct option is D a2+2ab+b2 c2 (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 bc + ca + cb c^2 = (a^2 + 2ab + b^2 c^2) ( ∵ a ...

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Byju's Answer

Standard VI

Mathematics

Multiplication of a Polynomial and Monomial

(a+b+c)(a+b-c...

Question

$(a + b + c) (a + b - c)$ = ___.

a²+2ab-c²

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a²+4ab+b²-c²

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a²+2ab+b²

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a²+2ab+b²-c²

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Solution

The correct option is D
a²+2ab+b²-c²

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

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

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Similar questions

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)

Q. Compute the following:
(i)

[\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]

(ii)

[\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]

(iii)

⎡ ⎢ ⎣ \begin{matrix} - 1 82 \end{matrix} \begin{matrix} 458 \end{matrix} \begin{matrix} - 6 165 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 1283 \end{matrix} \begin{matrix} 702 \end{matrix} \begin{matrix} 654 \end{matrix} ⎤ ⎥ ⎦

(iv)

[\begin{matrix} {cos}^{2} x & {sin}^{2} x {sin}^{2} x & {cos}^{2} x \end{matrix}] + [\begin{matrix} {sin}^{2} x & {cos}^{2} x {cos}^{2} x & {sin}^{2} x \end{matrix}]

Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Divide:
$[(a^{2} + 2 a b + b^{2}) - (a^{2} + 2 a c + c^{2})]$ by $2 a + b + c$

Compute the following:

(i) (ii)

(iii)

(v)

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(a+b+c)(a+b−c) = ___.

The correct option is D a2+2ab+b2-c2 (a+b+c)(a+b−c) =a(a+b−c)+b(a+b−c)+c(a+b−c) =a2+ab−ac+ba+b2−bc+ca+cb−c2 =(a2+2ab+b2−c2) ( ∵ac=ca and bc=cb )

$(a + b + c) (a + b - c)$ = ___.

The correct option is D
a²+2ab+b²-c²

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

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