Expand the following, using suitable identities:

${(2 x - y + z)}^{2}$ [3 MARKS]

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Solution

Formula: 1 Mark
Application: 2 Marks

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

Using the identity

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

$a = 2 x, b = - y, c = z$

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

$= {4 x}^{2} + {(y)}^{2} + {(z)}^{2} - 4 x y - 2 y z + 4 x z$

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