Expanding the Expression: (x+4)(x^2 + 7x)
This article will guide you through the process of expanding the expression (x+4)(x^2 + 7x). This is an example of multiplying two binomials, one of which is a trinomial. We can achieve this using the distributive property.
The Distributive Property
The distributive property states that a(b + c) = ab + ac. This means we can distribute the factor outside the parentheses to each term inside the parentheses.
Expanding the Expression

Distribute the first term:
 Multiply x by each term in the second parentheses:
 x * x^2 = x^3
 x * 7x = 7x^2
 Multiply x by each term in the second parentheses:

Distribute the second term:
 Multiply 4 by each term in the second parentheses:
 4 * x^2 = 4x^2
 4 * 7x = 28x
 Multiply 4 by each term in the second parentheses:

Combine the terms:
 We now have: x^3 + 7x^2 + 4x^2 + 28x
 Combine like terms: x^3 + 11x^2 + 28x
Final Answer
Therefore, the expanded form of (x+4)(x^2 + 7x) is x^3 + 11x^2 + 28x.