Factorize $x (x + z) - y (y + z)$

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Solution

$\begin{matrix} x (x + z) - y (y + z) & = x^{2} + x z - y^{2} - y z = x^{2} - y^{2} + x z - y z = (x - y) (x + y) + z (x - y) = (x - y) (x + y + z) \end{matrix}$

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Similar questions

|\begin{matrix} z & x & y \\ z^{2} & x^{2} & y^{2} \\ z^{4} & x^{4} & y^{4} \end{matrix}| = |\begin{matrix} x & y & z \\ x^{2} & y^{2} & z^{2} \\ x^{4} & y^{4} & z^{4} \end{matrix}| = |\begin{matrix} x^{2} & y^{2} & z^{2} \\ x^{4} & y^{4} & z^{4} \\ x & y & z \end{matrix}| = x y z (x - y) (y - z) (z - x) (x + y + z) .

(y - z) (z + x) = 22

(z + x) (x - y) = 33

(x - y) (y - z) = 6

ω ∣ ∣ ∣ ∣ ∣ \begin{matrix} x & y & z x^{2} & y^{2} & z^{2} y + z & z + x & x + y \end{matrix} ∣ ∣ ∣ ∣ ∣ = (x - y) (y - z) (z - x) (x + y + z)

(x + y) (y + z) = 35, (y + z) (z + x) = 56

(z + x) (x + y) = 40

x, y

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