Expand each of the following , using suitable identities :
${(3 a - 7 b - c)}^{2}$

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Solution

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$(3 a - 7 b - c)^{2} = (3 a)^{2} + (- 7 b)^{2} + (- c)^{2} + 2 (3 a)) (- 7 b) + 2 (- 7 b) (- c) + 2 (- c) (3 a)$
$= 9 a^{2} + 49 b^{2} + c^{2} - 42 a b + 14 b c - 6 a c$

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Expand the following, using suitable identities:
$1) {(3 a - 7 b - c)}^{2}$ .
$2) {(x + 2 y + 4 z)}^{2}$ [4 MARKS]

1) {(3 a - 7 b - c)}^{2}

2) {(x + 2 y + 4 z)}^{2}

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