Evaluate the product (3a - 5b).(2a + 7b)

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Solution

We have, $(3 a - 5 b) . (2 a + 7 b)$
$= (3 a) . (2 a + 7 b) - (5 b) . (2 a + 7 b)$
$= 6 (a . a) + 21 (a . b) - 10 (b . a) - 35 (b . b)$
$= 6 | a |^{2} + 11 (a . b) - 35 | b |^{2}$ $(∵ a . a = | a |^{2} a n d a . b = b . a)$

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