(3d+5)(5d-1)-(6d-3)(2-8d)

2 min read Jun 16, 2024

Expanding and Simplifying the Expression (3d+5)(5d-1)-(6d-3)(2-8d)

This article will guide you through the process of expanding and simplifying the algebraic expression: (3d+5)(5d-1)-(6d-3)(2-8d).

We will use the distributive property (also known as the FOIL method) to expand the products:

(3d+5)(5d-1)
- (3d * 5d) + (3d * -1) + (5 * 5d) + (5 * -1) = 15d² - 3d + 25d - 5
(6d-3)(2-8d)
- (6d * 2) + (6d * -8d) + (-3 * 2) + (-3 * -8d) = 12d - 48d² - 6 + 24d

Now, let's combine the like terms from both expanded expressions:

15d² - 3d + 25d - 5 - (12d - 48d² - 6 + 24d)

Remember to distribute the negative sign:

15d² - 3d + 25d - 5 - 12d + 48d² + 6 - 24d

Combine the d² terms, d terms, and constant terms:

(15d² + 48d²) + (-3d + 25d - 12d - 24d) + (-5 + 6)

After combining the like terms, we get the simplified expression:

63d² - 14d + 1

Therefore, the expanded and simplified form of the expression (3d+5)(5d-1)-(6d-3)(2-8d) is 63d² - 14d + 1.