Final Answer:
The product of (n-3)(5n-2) is 5n^2 - 17n + 6.
Step-by-step explanation:
To find the product of the given binomials, we use the distributive property, which states that for any numbers a, b, and c, a(b + c) is equal to ab + ac. Applying this property to the given expression, we distribute the terms of the first binomial (n-3) to each term of the second binomial (5n-2):
(n-3)(5n-2) = n(5n) + n(-2) + (-3)(5n) + (-3)(-2)
Now, simplify each term:
= 5n^2 - 2n - 15n + 6
Combine like terms:
= 5n^2 - 17n + 6
So, the final answer is 5n^2 - 17n + 6, which represents the product of the given binomials. This is a quadratic expression in standard form, where the coefficients are 5, -17, and 6 for the squared, linear, and constant terms, respectively.