$a - [- {- (a - ¯ ¯¯¯¯¯¯¯¯¯ ¯ b - c)}] =$

c - b

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b - c

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2 a + b - c

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2 a - b + c

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Solution

The correct option is B $b - c$
$a - [- {- (a - ¯ ¯¯¯¯¯¯¯¯¯ ¯ b - c)}]$
$= a - [- {- (a - b + c)}]$ ........(removing bar brackets)
$= a - [- {- a + b - c}]$ .......(removing small brackets)
$= a - [a - b + c]$ .........(removing curly brackets)
$= a - a + b - c$ ........(removing square brackets)
$= b - c$

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Similar questions

|\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}

Verify the cyclic symmetry of the following expressions if a, b and c are the variables:

(1) a(b − c) + b(c − a) + c(a − b)

(2) ab(a + b) + bc(b + c) + ca(c + a)

(3) a²b(a − b) + b²c(b − c) + c²a(c − a)

(4) a²(a + b) + b²(b + c) + c²(c + a)

(5) ab²(a − b) + bc²(b − c) + ca²(c − a)

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