IS the statement true? $a^{2} (a - b + c) + b^{2} (a + b - c) - c^{2} (a - b - c)$ = $a^{3} + b^{3} + c^{3} - a^{2} b + a b^{2} - b^{2} c + c^{2} b + a^{2} c - a c^{2}$

True

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False

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Solution

The correct option is A True
We find the value of the given expression $a^{2} (a - b + c) + b^{2} (a + b - c) - c^{2} (a - b - c)$ as shown below:

$a^{2} (a - b + c) + b^{2} (a + b - c) - c^{2} (a - b - c) = a^{3} - a^{2} b + a^{2} c + b^{2} a + b^{3} - b^{2} c - c^{2} a + c^{2} b + c^{3} = a^{3} + b^{3} + c^{3} - a^{2} b + a^{2} c + b^{2} a - b^{2} c - c^{2} a + c^{2} b = a^{3} + b^{3} + c^{3} - a^{2} b + a b^{2} - b^{2} c + c^{2} b + a^{2} c - a c^{2}$

Hence, $a^{2} (a - b + c) + b^{2} (a + b - c) - c^{2} (a - b - c) = a^{3} + b^{3} + c^{3} - a^{2} b + a b^{2} - b^{2} c + c^{2} b + a^{2} c - a c^{2}$ .

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Similar questions

A = a^{2} b + a b^{2} - a^{2} c - a c^{2},

B = b^{2} c + b c^{2} - a^{2} b - a b^{2}

C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

a > b > c > 0

A x^{2} + B x + C = 0

a, b, c

A, B, C

A = a^{2} b + a b^{2} - a^{2} c - a c^{2}, B = b^{2} c + b c^{2} - a^{2} b - a b^{2}, C = a^{2} c + a c^{2} - b^{2} c - b c^{2}

a > b > c > 0

A x^{2} + B x + C = 0

a, b, c

a^{2} b^{2} c^{2} (a^{- 3} + b^{- 3} + c^{- 3}) = (a^{3} + b^{3} + c^{3})

∣ ∣ ∣ ∣ \begin{matrix} b + c & a - b & a c + a & b - c & b a + b & c - a & c \end{matrix} ∣ ∣ ∣ ∣ =

If $a, b, c$ are in G.P., then ___.

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