Final answer:
To multiply the given expressions, we can apply the distributive property. By multiplying each term in the first expression by each term in the second expression and combining like terms, we obtain the expression 2x⁴ + 4x³ + 17x² - 7x + 5.
Step-by-step explanation:
To multiply the two given expressions, we can apply the distributive property. We multiply each term in the first expression by each term in the second expression, and then combine like terms. Following this process, we get:
(x² + 3x + 5)(2x² - 2x + 1) = x²(2x² - 2x + 1) + 3x(2x² - 2x + 1) + 5(2x² - 2x + 1)
= 2x⁴ - 2x³ + x² + 6x³ - 6x² + 3x + 10x² - 10x + 5
= 2x⁴ + 4x³ + 17x² - 7x + 5
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