To multiply a and b, we first distribute a to each term in b:
a * b = (3x² - 2x + 3)(x³ - x² + 6x + 3)
Now, we multiply each term in the first expression by each term in the second expression:
= 3x² * x³ - 3x² * x² + 3x² * 6x + 3x² * 3
2x * x³ + 2x * x² - 2x * 6x - 2x * 3
3 * x³ - 3 * x² + 3 * 6x + 3 * 3
Simplify each term:
= 3x^5 - 3x^4 + 18x^3 + 9x²
2x^4 + 2x³ - 12x² - 6x
3x³ - 3x² + 18x + 9
Combine like terms:
= 3x^5 - 5x^4 + 17x^3 + 6x² + 12x + 9
Therefore, a * b = 3x^5 - 5x^4 + 17x^3 + 6x² + 12x + 9