(2n^2+5n+3)(4n-5)

less than a minute read Jun 16, 2024

Expanding and Simplifying the Expression (2n^2 + 5n + 3)(4n - 5)

This expression involves multiplying two polynomials. We can simplify it by using the distributive property (also known as FOIL method).

1. Applying the Distributive Property

First: Multiply the first terms of each binomial: (2n^2)(4n) = 8n^3
Outer: Multiply the outer terms: (2n^2)(-5) = -10n^2
Inner: Multiply the inner terms: (5n)(4n) = 20n^2
Last: Multiply the last terms: (5n)(-5) = -25n
Constant: Multiply the constant terms: (3)(4n) = 12n
Constant: Multiply the constant terms: (3)(-5) = -15

2. Combining Like Terms

Now, we have the following expression:

8n^3 - 10n^2 + 20n^2 - 25n + 12n - 15

Combining the like terms, we get:

8n^3 + 10n^2 - 13n - 15

Therefore, the simplified form of the expression (2n^2 + 5n + 3)(4n - 5) is 8n^3 + 10n^2 - 13n - 15.