Expanding the Expression: (d+6)(2d^2−d+7)
This article will guide you through the process of expanding the expression (d+6)(2d^2−d+7). This involves applying the distributive property, also known as the FOIL method, to simplify the expression.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number. In this context, we'll be distributing each term in the first binomial, (d+6), to each term in the second binomial, (2d^2−d+7).
Expanding the Expression

Distribute 'd':
 d * 2d^2 = 2d^3
 d * d = d^2
 d * 7 = 7d

Distribute '6':
 6 * 2d^2 = 12d^2
 6 * d = 6d
 6 * 7 = 42

Combine Like Terms:
 2d^3 + (d^2) + 12d^2 + 7d + (6d) + 42 = 2d^3 + 11d^2 + d + 42
Final Result
Therefore, the expanded form of the expression (d+6)(2d^2−d+7) is 2d^3 + 11d^2 + d + 42.
Remember: You can always verify your answer by plugging in a value for 'd' into both the original expression and the expanded expression. The results should be the same.