(d^2+3)(d^2+2d+1)=

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (d^2 + 3)(d^2 + 2d + 1)

This problem involves expanding a product of two quadratic expressions. We can achieve this by using the distributive property (also known as FOIL).

FOIL stands for:

• First: Multiply the first terms of each binomial.
• Outer: Multiply the outer terms of the binomials.
• Inner: Multiply the inner terms of the binomials.
• Last: Multiply the last terms of each binomial.

Let's apply FOIL to our expression:

(d^2 + 3)(d^2 + 2d + 1)

• First: (d^2)(d^2) = d^4
• Outer: (d^2)(2d) = 2d^3
• Inner: (3)(d^2) = 3d^2
• Last: (3)(2d) = 6d
• Last: (3)(1) = 3

Now, combine the terms:

d^4 + 2d^3 + 3d^2 + 6d + 3

Therefore, the expanded form of (d^2 + 3)(d^2 + 2d + 1) is d^4 + 2d^3 + 3d^2 + 6d + 3.