Expand the following expression: $(x + 2 y - z)^{2}$

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Solution

We know that $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
Here, $a = x, b = 2 y, c = - z$
$∴ (x + 2 y - z)^{2} = x^{2} + (2 y)^{2} + (- z)^{2} + 2. x .2 y + 2.2 y . (- z) + 2. (- z) . x$
$=$ $x^{2} + 4 y^{2} + z^{2} + 4 x y - 4 y z - 2 x z$

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