Expanding the Expression: (d^2 + 1)(2d^2  5d + 7)
This article will explore how to expand the given expression: (d^2 + 1)(2d^2  5d + 7). We'll use the distributive property to multiply each term in the first factor by each term in the second factor.
Expanding using the Distributive Property
The distributive property states that for any real numbers a, b, and c: a(b + c) = ab + ac. We can apply this to our expression:

Distribute the first term of the first factor: (d^2)(2d^2  5d + 7) = 2d^4  5d^3 + 7d^2

Distribute the second term of the first factor: (1)(2d^2  5d + 7) = 2d^2  5d + 7

Combine the results: 2d^4  5d^3 + 7d^2 + 2d^2  5d + 7

Simplify by combining like terms: 2d^4  5d^3 + 9d^2  5d + 7
Final Expanded Form
Therefore, the expanded form of (d^2 + 1)(2d^2  5d + 7) is 2d^4  5d^3 + 9d^2  5d + 7.