Expanding the Expression (d^2 + 3)(d^2 + 2d + 1)
This article will guide you through expanding the given expression using the distributive property and simplifying the result.
Understanding the Distributive Property
The distributive property states that:
a(b + c) = ab + ac
This property allows us to multiply a single term by multiple terms within parentheses.
Expanding the Expression

Distribute the first term (d^2) from the first parenthesis: (d^2 + 3)(d^2 + 2d + 1) = d^2(d^2 + 2d + 1) + 3(d^2 + 2d + 1)

Distribute the second term (3) from the first parenthesis: = d^4 + 2d^3 + d^2 + 3d^2 + 6d + 3

Combine like terms: = d^4 + 2d^3 + 4d^2 + 6d + 3
Final Result
Therefore, the expanded and simplified form of the expression (d^2 + 3)(d^2 + 2d + 1) is d^4 + 2d^3 + 4d^2 + 6d + 3.