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

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Solution

$(- 2 x + 5 y - 3 z)^{2}$ is of the form $(a + b + c)^{2}$

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

where $a = - 2 x, b = 5 y, c = - 3 z$

$∴ (- 2 x + 5 y - 3 z)^{2} = (- 2 x)^{2} + (5 y)^{2} + (- 3 z)^{2} + 2 (- 2 x) (5 y) + 2 (5 y) (- 3 z) + 2 (- 3 z) (- 2 x)$

$= 4 x^{2} + 25 y^{2} + 9 z^{2} - 20 x y - 30 y z + 12 z x$ .

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