Simplify $(4 a + 5 b) (6 a - 7 b) - (a + 2 b + 3) (8 a - 11)$

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Solution

$(4 a + 5 b) (6 a - 7 b) - (a + 2 b + 3) (8 a - 11) = 24 a b + 30 a b - 28 a b - 35 a b - [8 a 2 - 11 a + 16 a b - 22 b + 24 a - 33]$
= - $9 a b - [8 a^{2} + 16 a b + 13 a - 22 b - 33]$
= $- 9 a b - 8 a^{2} - 16 a b - 13 a + 22 b + 33$
= $- 8 a^{2} - 25 a b - 13 a + 22 b + 33$

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