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

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Solution

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

Here a = -2x, b = 5y and c = -3z

= ${(- 2 x)}^{2}$ + ${(5 y)}^{2}$ + ${(- 3 z)}^{2}$ + 2(-2x)(5y) + 2(5y)(-3z) + 2(-3z)(-2x) (Expanding using ( $a + b + c)^{2}$ = $a^{2}$ + $b^{2}$ + $c^{2}$ + 2ab + 2bc + 2ca )

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

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