Simplify:
(5x − 3)(x + 2) − (2x + 5)(4x − 3)

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Solution

To simplify, we will proceed as follows:

$(5 x - 3) (x + 2) - (2 x + 5) (4 x - 3) = [(5 x - 3) (x + 2)] - [(2 x + 5) (4 x - 3)]$
$= [5 x (x + 2) - 3 (x + 2)] - [2 x (4 x - 3) + 5 (4 x - 3)]$ (Distributive law)
$= 5 x^{2} + 10 x - 3 x - 6 - 8 x^{2} + 6 x - 20 x + 15$
$= 5 x^{2} - 8 x^{2} + 10 x - 3 x + 6 x - 20 x - 6 + 15$ (Rearranging)
$= 5 x^{2} - 8 x^{2} + 10 x - 3 x + 6 x - 20 x - 6 + 15 = - 3 x^{2} - 7 x + 9$ (Combining like terms)

Hence, the answer is $- 3 x^{2} - 7 x + 9$ .

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