Evaluate: $(x + 2 y) (- 3 x - y) - (x + y) (x - y) + (x - 2 y) (- 2 x + y)$

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Solution

$(x + 2 y) (- 3 x - y) - (x + y) (x - y) + (x - 2 y) (- 2 x + y)$
$= - 3 x^{2} - x y - 6 x y - 2 y^{2} - x^{2} + y^{2} - 2 x^{2} + x y + 4 x y - 2 y^{2}$
$= - 6 x^{2} - 3 y^{2} - 2 x y$
$= - (6 x^{2} + 2 x y - 3 y^{2})$

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∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{z} & \frac{1}{z} & - \frac{(x + y)}{z^{2}} - \frac{(y + z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} - \frac{y (y + z)}{x^{2} z} & \frac{x + 2 y + z}{x z} & - \frac{y (x + y)}{x z^{2}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

Try simplifying these:

(i) (3x + 2y) − (x + y)

(ii) (3x + 2y) − (x − y)

(iii) (x + y) − (x − y)

(iv) (x − y) − (x + y)

(v) (4x − 3y) − (2x − 5x)

(2 x - 3 y) (3 x + y) + (x + 2 y) (x - y)

x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1, x^{3} - 1, x^{3} + x^{2} + x

x^{2} y + y x + y

\frac{d y}{d x} = \frac{x + y + 1}{2 x + 2 y + 3}

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