Find the value of $a^{2} + b^{2} + c^{2} - a b - a c - b c$
When $a = x + y, b = x - y$ and $c = x + 2 y$

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Solution

Given
$a = x + y, b = x - y, c = x + 2 y$
And required equation,
$a^{2} + b^{2} + c^{2} - a b - a c - b c$
On putting the given values equation
We get,
$= 7 y^{2}$

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Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} x & y & z y & z & x z & x & y \end{matrix} ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} r & s & s s & r & s s & s & r \end{matrix} ∣ ∣ ∣ ∣

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