Expand the following, using suitable identities:
$1) {(- 2 x + 3 y + 2 z)}^{2}$
$2) {(- 2 x + 5 y - 3 z)}^{2}$ . [4 MARKS]

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Solution

Formula: 1 Mark
Application: 1 Mark each
Answer: 0.5 Mark each

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

$1) {(- 2 x + 3 y + 2 z)}^{2}$

$a = - 2 x, b = 3 y, c = 2 z$ [comparing with identity(i)]

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

$= {4 x}^{2} + {9 y}^{2} + {4 z}^{2} - 12 x y + 12 y z - 8 z x$

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

$a = - 2 x, b = 5 y, c = - 3 z$ [comparing with identity(i)]

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

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

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