Final answer:
To solve the expression to a polynomial in standard form, we need to multiply the two polynomials: (3x+1)(2x²+9x+6). Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial and combine like terms to get the polynomial in standard form.
Step-by-step explanation:
To solve the expression to a polynomial in standard form, we need to multiply the two polynomials: (3x+1)(2x²+9x+6).
Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial:
3x * 2x² = 6x³
3x * 9x = 27x²
3x * 6 = 18x
1 * 2x² = 2x²
1 * 9x = 9x
1 * 6 = 6
Combining like terms, we get:
6x³ + 27x² + 18x + 2x² + 9x + 6
Finally, we simplify the polynomial by adding like terms:
6x³ + (27x² + 2x²) + (18x + 9x) + 6
This gives us the polynomial in standard form: 6x³ + 29x² + 27x + 6.