Final answer:
To simplify the expression (3x + 2)(2x + 3) - (4x - 3)(2x - 1), expand both sets of parentheses and subtract the second expanded expression from the first, resulting in -2x² + 23x + 3.
Step-by-step explanation:
To simplify the expression (3x + 2)(2x + 3) - (4x - 3)(2x - 1), we need to expand the parentheses and combine like terms. First, we use the distributive property (also known as the FOIL method in this case) to multiply the terms within each set of parentheses:
(3x + 2)(2x + 3) = 6x² + 9x + 4x + 6 = 6x² + 13x + 6
(4x - 3)(2x - 1) = 8x² - 4x - 6x + 3 = 8x² - 10x + 3
Now subtract the second expanded expression from the first:
6x² + 13x + 6 - (8x² - 10x + 3)
This equals 6x² + 13x + 6 - 8x² + 10x - 3, which simplifies to -2x² + 23x + 3.