Find- -a-b-c-a-b-c- -a-2 nbsp- 2ab - c-2-a-2 nbsp- 4ab - b-2 nbsp- c-2-a-2 nbsp- 2ab - b-2-a-2 nbsp- 2ab - b-2 nbsp- c-2-

The correct option is D a^2 nbsp;+ 2ab + b^2 nbsp; c^2 (a+b+c)×(a+b c) =(a^2 nbsp;+ ab nbsp;ac + ab + b^2 nbsp; bc + nbsp;ac + bc c^2) = (a^2 ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Any Polynomial

Find: (a+b+c)...

Question

Find:
$(a + b + c) \times (a + b - c) =$

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

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$a^{2} + 4 a b + b^{2} - c^{2}$

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

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

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Solution

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

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

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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)

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 $2 a + b + c$

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}]

Compute the following:

(i) (ii)

(iii)

(v)

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Find: (a+b+c)×(a+b−c)=

The correct option is D a2+2ab+b2−c2 (a+b+c)×(a+b−c) =(a2+ab−ac+ab+b2−bc+ac+bc−c2) =(a2+2ab+b2−c2)

Find:
$(a + b + c) \times (a + b - c) =$

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

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