Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)

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Solution

To simplify, we will proceed as follows:

$(3 x - 2) (2 x - 3) + (5 x - 3) (x + 1) = [(3 x - 2) (2 x - 3)] + [(5 x - 3) (x + 1)]$
$= [3 x (2 x - 3) - 2 (2 x - 3)] + [5 x (x + 1) - 3 (x + 1)]$ (Distributive law)
$= 6 x^{2} - 9 x - 4 x + 6 + 5 x^{2} + 5 x - 3 x - 3$
$= 6 x^{2} + 5 x^{2} - 9 x - 4 x + 5 x - 3 x - 3 + 6$ (Rearranging)
$= 11 x^{2} - 11 x + 3$ (Combining like terms)

Thus, the answer is $11 x^{2} - 11 x + 3$ .

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