Simplifying Expressions: (5d^2+8d+1)(2d^2+3d1)
This article will guide you through the process of simplifying the expression (5d^2+8d+1)(2d^2+3d1).
Understanding the Steps
To simplify this expression, we will follow these steps:
 Distribute the negative sign: The minus sign before the second set of parentheses means we multiply each term inside the second set of parentheses by 1.
 Combine like terms: After distributing the negative sign, we combine terms with the same variable and exponent.
Simplifying the Expression
Let's break down the process:

Distribute the negative sign: (5d^2 + 8d + 1) + (1 * 2d^2) + (1 * 3d) + (1 * 1)

Simplify: 5d^2 + 8d + 1  2d^2  3d + 1

Combine like terms: (5d^2  2d^2) + (8d  3d) + (1 + 1)

Simplify further: 3d^2 + 5d + 2
Final Result
Therefore, the simplified form of the expression (5d^2+8d+1)(2d^2+3d1) is 3d^2 + 5d + 2.