Final answer:
To expand and simplify the expression (5x+3)(3x-2)(x+3), first multiply (5x+3) and (3x-2) to get 15x² - x - 6, and then multiply this by (x+3) to find the final expanded and simplified form, which is 15x³ + 44x² - 9x - 18.
Step-by-step explanation:
To expand and simplify the expression (5x+3)(3x-2)(x+3), we'll need to perform polynomial multiplication. First, we'll expand two of the three binomials, and then multiply the result by the remaining binomial. Here's how:
Multiply the first two binomials: (5x+3)(3x-2).
- 5x * 3x = 15x²
- 5x * (-2) = -10x
- 3 * 3x = 9x
- 3 * (-2) = -6
Combine like terms: 15x² - 10x + 9x - 6 = 15x² - x - 6.
Now multiply this trinomial by the remaining binomial (x+3).
- (15x² - x - 6)(x + 3)
- 15x² * x = 15x³
- 15x² * 3 = 45x²
- -x * x = -x²
- -x * 3 = -3x
- -6 * x = -6x
- -6 * 3 = -18
Combine all the like terms to get the final expanded form: 15x³ + 45x² - x² - 3x - 6x - 18.
Simplify: 15x³ + 44x² - 9x - 18.