Expand $(2 x - 5 y - 7 z)^{2}$ .

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Solution

Expanding the given expression:
The given expression is $(2 x - 5 y - 7 z)^{2}$ .
Use identity, $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$ to expand.
The given equation can be rewritten as ${(2 x - 5 y - 7 z)}^{2} = {[2 x + (- 5 y) + (- 7 z)]}^{2}$ .
Compare the given expression with the identity we get, $a = 2 x, b = - 5 y, c = - 7 z$ .
Substitute values in identity we get:
${[2 x + (- 5 y) + (- 7 z)]}^{2} = {(2 x)}^{2} + {(- 5 y)}^{2} + {(- 7 z)}^{2} + 2 (2 x) (- 5 y) + 2 (- 5 y) (- 7 z) + 2 (x) (- 7 z) = 4 x^{2} + 25 y^{2} + 49 z^{2} - 20 x y + 70 y z - 28 x z$
Hence, the expression, ${(2 x - 5 y - 7 z)}^{2} = 4 x^{2} + 25 y^{2} + 49 z^{2} - 20 x y + 70 y z - 28 x z$ .

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