Final answer:
To multiply the polynomials (6x²+3x+5) and (3x²+5x), apply the distributive property, and combine like terms to obtain the final result 18x⁴ + 39x³ + 30x² + 25x.
Step-by-step explanation:
To multiply the polynomials (6x²+3x+5) and (3x²+5x), we need to use the distributive property, also known as the FOIL (First, Outer, Inner, Last) method for the first two terms of each polynomial and then apply a similar process for the remaining terms.
Step-by-step multiplication:
- Multiply the First terms: (6x²) * (3x²) = 18x⁴
- Multiply the Outer terms: (6x²) * (5x) = 30x³
- Multiply the Inner terms: (3x) * (3x²) = 9x³
- Multiply the Last terms: (3x) * (5x) = 15x²
- Multiply the constant term (5) by each term of the second polynomial: (5) * (3x²) = 15x², and (5) * (5x) = 25x
Combine like terms:
18x⁴ + 30x³ + 9x³ + 15x² + 15x² + 25x
18x⁴ + (30x³ + 9x³) + (15x² + 15x²) + 25x
18x⁴ + 39x³ + 30x² + 25x
The final result is: 18x⁴ + 39x³ + 30x² + 25x