Final answer:
To multiply the expression (9x-2)(3x-8), we use the distributive property and combine like terms. The standard form of the product is 27x^2 - 78x + 16.
Step-by-step explanation:
To multiply the expression (9x-2)(3x-8), we can use the distributive property of multiplication over addition/subtraction. We multiply each term in the first expression (9x-2) by each term in the second expression (3x-8) and combine like terms. Here's the step-by-step calculation:
- Multiplying 9x from the first expression by 3x from the second expression gives 27x^2.
- Multiplying 9x from the first expression by -8 from the second expression gives -72x.
- Multiplying -2 from the first expression by 3x from the second expression gives -6x.
- Multiplying -2 from the first expression by -8 from the second expression gives 16.
Combining these terms, the product is 27x^2 - 72x - 6x + 16, which can be simplified to 27x^2 - 78x + 16. This is the standard form of the expression.