Final answer:
To find the product of (x-9)(x²+9x+81), we use the distributive property to multiply each term in the first expression by each term in the second, simplifying the result to x³ - 81x - 729.
Step-by-step explanation:
The question asks to find the product of the binomial (x-9) multiplied by the trinomial (x²+9x+81). To simplify the expression, we use the distributive property also known as the FOIL method (First, Outside, Inside, Last) to multiply each term in the first binomial by each term in the second trinomial. This results in a polynomial of higher degree.
Step-by-step multiplication:
• First, multiply the first terms: x * x² = x³
• Outside terms: x * 9x = 9x²
• Inside terms: -9 * x² = -9x²
• Last terms: -9 * 9x = -81x
• Multiply -9 by 81: -9 * 81 = -729
Combine like terms:
• x³ term remains the same.
• Combine 9x² and -9x² which cancel each other out.
• Combine -81x term.
• The constant -729 remains unchanged.
The simplified result is x³ - 81x - 729.