Final answer:
The product of 5x³ and xy⁴ - 2x³y is 5x⁴y⁴ - 10x⁶y. This is found by distributing 5x³ over each term in the parentheses and combining the results.
Step-by-step explanation:
To find the product of 5x³ and xy⁴ - 2x³y, we apply the distributive property of multiplication over subtraction. We multiply 5x³ by each term inside the parentheses.
Firstly, 5x³ × xy⁴ = 5x⁴y⁴ (since x³ × x is x⁴ and the y terms are only in the second multiplier).
Secondly, 5x³ × (-2x³y) = -10x⁶y (Multiplying the coefficients 5 and -2 gives -10, and x³ × x³ is x⁶ because we add the exponents). The product of 5x³ and xy⁴ - 2x³y can be found by multiplying each term in 5x³ by every term in xy⁴ - 2x³y. Using the distributive property, we get:
5x³ * xy⁴
5x³ * (-2x³y)
When we simplify these expressions, we get:
5x⁴y⁴
-10x⁶y²
Combining these terms, the product of 5x³ and xy⁴ - 2x³y is 5x⁴y⁴ - 10x⁶y². Therefore, the correct answer is option a. 5x⁴y⁴ - 10x⁶y².
Combining both gives us the final expression: 5x⁴y⁴ - 10x⁶y.