Simplify using suitable identities:
$(- 2 x + 5 y - 3 z)^{2}$

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Solution

We have ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
where $a = - 2 x, b = 5 y, c = - 3 z$
$∴ {(- 2 x + 5 y - 3 z)}^{2} = {(- 2 x)}^{2} + {(5 y)}^{2} + {(- 3 z)}^{2} + 2 \times - 2 x \times 5 y + 2 \times 5 y \times - 3 z + 2 \times - 3 z \times - 2 x$
$= 4 x^{2} + 25 y^{2} + 9 z^{2} - 20 x y - 30 y z + 12 x z$

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