(a+b+c)×(a+b c) = ((a)×(a+b c))+((b)×(a+b c))+((c)×(a+b c)) =(a^2 nbsp;+ ab nbsp;ac + ab + b^2 nbsp; bc + nbsp;ac + bc c^2) = (a^2 nbsp;+ 2ab + ...

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Applying Difference of Squares as a Product of Its Sum and Difference

Find:a+b+c×a+...

Question

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

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

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

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

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

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Solution

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

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

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

Suggest Corrections

Similar questions

Find:

(a) $\frac{1}{2}$ of (i) $24$ (ii) $46$

\frac{2}{3}

18

27

\frac{3}{4}

16

36

\frac{4}{5}

20

35

|\begin{matrix} a + b & b + c & c + a \\ b + c & c + a & a + b \\ c + a & a + b & b + c \end{matrix}| = 2 |\begin{matrix} a & b & c \\ b & c & a \\ c & a & b \end{matrix}|

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

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

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

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