Question:
Simplify:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
Solution:
To simplify, we will proceed as follows:
(3x − 2)(2x − 3) + (5x − 3)(x + 1)
$=[(3 x-2)(2 x-3)]+[(5 x-3)(x+1)]$
$=[3 x(2 x-3)-2(2 x-3)]+[5 x(x+1)-3(x+1)] \quad$ (Distributive law)
$=6 x^{2}-9 x-4 x+6+5 x^{2}+5 x-3 x-3$
$=6 x^{2}+5 x^{2}-9 x-4 x+5 x-3 x-3+6 \quad$ (Rearranging)
$=11 x^{2}-11 x+3 \quad$ (Combining like terms)
Thus, the answer is $11 x^{2}-11 x+3$.